Section outline


  •  Key unit competence: Evaluate the atomic models and photoelectric 
                                                  effect
     Unit Objectives:
      By the end of this unit I will be able to;
     ◊ Describe different atomic models by explaining their concepts and 
    drawbacks. 
    ◊ Explain the photoelectric effect and its applications in everyday life.

    Introductory Activity


    1. Basing on the figure above,
     a. How is the structure/arrangement of balls shown in the figure 
    related to an atom? You can use chemistry knowledge from 
    O’level.
     b. Relate the arrangement of electrons in an atom to how the 
    balls in the figure above are arranged.
     c. Explain how movement of particles in an atom leads to release 
    or absorption of energy
    4. It is important to realise that a lot of what we know about the 
    structure of atoms has been developed over a long period of time. 
    This is often how scientific knowledge develops, with one person 
    building on the ideas of someone else.In attempt to explain an 
    atom, different scientists suggest different models. An atomic model 
    represents what the structure of an atom could look like, based on 
    what we know about how atoms behave. It is not necessarily a true 
    picture of the exact structure of an atom. 
    a. Why did these scientists use the word Model not exact structure 
    of an atom?
     b. Can you explain some of the scientific models that tried to 
    explain the structure of an Atom?

         9.0 INTRODUCTION
     An atomic theory is a model developed to explain the properties and 
    behaviours of atoms. An atomic theory is based on scientific evidence 
    available at any given time and serves to suggest future lines of research 
    about atoms.
     The concept of an atom can be traced to debate among Greek philosophers 
    that took place around the sixth century B.C. One of the questions that 
    interested these thinkers was the nature of matter. Is matter continuous 
    or discontinuous? If you could break a piece of chalk as long as you wanted, 
    would you ever reach some ultimate particle beyond which further division 
    was impossible? Or could you keep up that process of division forever?
     Such questions need the knowledge on the atomic structure and interaction 
    with photoelectric effect to be answered. This theory is helpful in Chemistry 
    (Atomic structure), Security (Alarm systems), Medicine, Archaeology, etc.
     
    9.1 STRUCTURE OF THE ATOM AND THOMSON’S     MODEL
     structure of the atom
     An atom is the smallest particle of an element that retains again the 
    characteristics or the properties of that element during chemical reaction.
     By the early 1900s scientists were able to break apart the atoms into 
    particles that they called the electron and the nucleus which is made of 
    proton and neutrons. 

    • Electrons 
    Electrons surround the dense nucleus of an atom. It is the smallest 
    subatomic particle with a mass of  
     and a negative electric charge. The electron is also one of the few
    elementary particles that is     stable, meaning it can exist by itself for a long period of time.
    Most other     elementary particles can exist independently for only a fraction of a second. 
    Electrons have no detectable shape or structure. 
    The electrons revolve around the nucleus in fixed trajectory (orbits) called 
    energy levels or shell. These shells have the names K, L, M, N, etc…
     The shell of atom just prior to the outermost shell of an atom cannot 
    accommodate more than 8 electrons even it has a capacity to accommodate 
    more electrons. The outermost shell (last shell) which contains electrons 
    is called the conduction shell or valence shell. On each electron shell, we 
    can meet  N=2n2 electrons, where N is the number of the electron shell. 
    The valence electrons which are not very attached to the nucleus are called 
    free electrons. The free electrons can be easily detached from the atom 
    by application of a small external energy (usually thermal energy by 
    increasing the temperature).

    • Protons 
    Proton is a subatomic particle with a positive charge. The charge is equal 
    and opposite to that of an electron. The mass of a proton is 1840 times 
    that of an electron. Thus the mass of an atom is mainly due to protons 
    and neutrons. The proton is one of the few elementary particles that are 
    stable—that is, it can exist by itself for a long period of time. The number of 
    protons is called the atomic number (Z).
     In normal atom, the number of electrons is equal to the number of protons. 
    The atomic number (Z) of an atom is equal to the number of protons (or 
    electrons) contained in atom. 

    •     Neutron 
    Neutron is a subatomic particle with a mass almost equal to the mass of a 
    proton. It has no electric charge. The neutron is about 10-13 cm in diameter 
    and weighs The number of protons and neutrons
    is called     nucleons number, or, alternatively, the mass number (A). The mathematical
    relationship     between atomic number (Z), mass number (A) and neutron number No is 


    Thomson’s model
     English scientist Joseph John Thomson’s cathode ray experiments (end 
    of the 19th century) led to the discovery of the negatively charged electron 
    and the first ideas of the structure of these indivisible atoms. In his model 
    of the atom, Sir J J Thomson (1856-1940) suggested a model of atom as
     “The atom is like a volume of positive charge with electrons embedded 

    throughout the volume, much like the seeds in watermelon.”Fig.9.4


    Success and Failure of Thomson’s model 
    Thomson’s model explained the phenomenon of thermionic emission, 
    photoelectric emission and ionization. The model fails to explain the 
    scattering of a-particles and it is the origin of spectral lines observed in the 
    spectrum of hydrogen and other atoms. 

    9.2 RUTHERFORD’S ATOMIC MODEL 
    Rutherford performed experiments on the scattering of alpha particles by 

    extremely thin gold foils and made the following observations;


    Note:
     • Some of a-particles are deflected through small angles. 
    • A few a-particles (1 in 1000) are deflected through the angle more 
    than 90°.
     • A few a-particles (very few) returned back i.e. deflected by 180°. 
    • Distance of closest approach (Nuclear dimension) is the minimum 
    distance from the nucleus up to which the a-particle approach. It is 
    denoted by r0  . From figure 


    From these experiments a new model of the atom was born called 
    Rutherford’s planetary model of the atom. The following conclusions were 
    made to describe the atomic structure:
     • Most of the mass and all of the charge of an atom is concentrated in a 
    very small region called atomic nucleus.
     • Nucleus is positively charged and it’s size is of the order of  10–15 m .
     • In an atom there is maximum empty space and the electrons revolve 
    around the nucleus in the same way as the planets revolve around the sun.
     
    Drawbacks : Rutherford's model could not explain the following:
     • Stability of atom: It could not explain the stability of atom because 
    according to classical electrodynamics, an accelerated charged particle 
    should continuously radiate energy. Thus, an electron moving in a 
    circular path around the nucleus should also radiate energy and thus 
    move into and smaller orbits of gradually decreasing radius and it 

    should ultimately fall into nucleus. 


    • According to this model, the spectrum of atom must be continuous 
    whereas practically it is a line spectrum.
     • It did not explain the distribution of electrons outside the nucleus.
     
    9.3 BOHR’S ATOMIC MODEL
    Bohr proposed a model for hydrogen atom which is also applicable for 
    some lighter atoms in which a single electron revolves around a stationary 
    nucleus of positive charge Ze (called hydrogen like atom). Bohr’s model is 
    based on the following postulates: 
    • Each electron moves in a circular orbit centered at the nucleus.
     • The centripetal force needed by the electron moving in a circle is 
    provided by electrostatic force of attraction between the nucleus and 
    electrons.

     • The angular momenta p of electrons are whole number multiples of 





    Drawbacks of Bohr’s atomic model
     • It is valid only for single valency atoms, e.g. : H, He+2, Li+, Na+1 etc.
     • Orbits were taken as circular but according to Sommerfield these are 
    elliptical.
     • Intensity of spectral lines could not be explained. 
    • Nucleus was taken as stationary but it also rotates on its own axis. 
    • It could not explain the minute structure in spectral lines. 
    • This does not explain the Zeeman effect (splitting up of spectral lines 
    in magnetic field) and Stark effect (splitting up in electric field)
     • This does not explain the doublets in the spectrum of some of the 
    atoms like sodium (5890x10-10m & 5896x 10-10m)

     9.4  ENERGY LEVELS AND SPECTRAL LINES OF 
    HYDROGEN
     When hydrogen atom is excited, it returns to its normal unexcited state (or 
    ground state) by emitting the energy it had absorbed earlier. This energy 
    is given out by the atom in the form of radiations of different wavelengths 
    as the electron jumps down from a higher orbit to a lower orbit. Transition 
    from different orbits causes different wavelengths. These constitute spectral 
    series which are characteristic of the atom emitting them. When observed 
    through a spectroscope, these radiations are imaged as sharp and straight 

    vertical lines of a single colour.


    The spectral lines arising from the transition of electron forms a spectra 
    series. Mainly there are five series and each series is named after its 
    discover as Lyman series, Balmer series, Paschen series, Brackett series 
    and Pfund series. First line of the series is called first member, for which 
    line wavelength is maximum (λmax). Last line of the series (n2= ∞) is called 
    series limit, for which line wavelength is minimum (λmin).


    9.5  THERMIONIC EMISSION ( THERMO ELECTRONIC 
    EMISSION)
     Thermionic emission means the discharge of electrons from heated materials. 
    It is widely used as a source of electrons in conventional electron tubes (e.g., 
    television picture tubes) in the fields of electronics and communications. The 
    phenomenon was first observed (1883) by Thomas A. Edison as a passage of 

    electricity from a filament to a plate of metal inside an incandescent lamp.


     In thermionic emission, the heat supplies some electrons with at least the 
    minimal energy required to overcome the attractive force holding them in 
    the structure of the metal. This minimal energy, called the work function, 
    is the characteristic of the emitting material and the state of contamination 

    of its surface.

    9.6 APPLICATIONS OF CATHODE RAYS
     9.6.1 Cathode ray oscilloscope
     The cathode-ray oscilloscope (CRO) is a common laboratory instrument that 
    provides accurate time and amplitude measurements of voltage signals over 
    a wide range of frequencies. Its reliability, stability and ease of operation 

    makes it suitable as a general purpose laboratory instrument. 


    The main part of the C.R.O. is a highly evacuated glass tube housing parts 
    which generates a beam of electrons, accelerates them, shapes them into 
    a narrow beam and provides external connections to the sets of plates 
    changing the direction of the beam. The heart of the CRO is a cathode-ray 

    tube shown schematically in Fig.9-10;


    Working of a C.R.O
     • An indirectly heated cathode provides a source of electrons for the 
    beam by ‘boiling’ them out of the cathode.
     • The anode is circular with a small central hole. The potential of anode 
    creates an electric field which accelerates the electrons, some of which 
    emerge from the hole as a fine beam. This beam lies along the central 
    axis of the tube.
     • The grid has the main function of concentrating the beam at the 
    centre controlling the potential of the grid that controls the number 
    of electrons for the beam, and hence the intensity of the spot on the 
    screen where the beam hits.
     • X and Y are two deflection plates. The X plates are used for deflecting 
    the beam from left to right (the x-direction) by means of the ‘ramp’ 
    voltage. The Y plates are used for deflection of the beam in the vertical 
    direction. Voltages on the X and Y sets of plates determine where the 
    beam will strike the screen and cause a spot of light.
     • The screen coated on the inside with a fluorescent material which 
    shines with green light (usually) where the electrons are striking.
     
    9.6.2 TV tubes
     The picture tube is the largest component of a television set, consisting 
    of four basic parts. The glass face panel is the screen on which images 
    appear. Suspended immediately behind the panel is a steel shadow mask, 
    perforated with thousands of square holes. (Connected to the mask is a 
    metal shield to neutralize disruptive effects of the Earth’s magnetic field.) 
    The panel is fused to a glass funnel, which comprises the rear of the picture 
    tube. The very rear of the funnel converges into a neck, to which an electron 

    gun assembly is connected.


    The inside of the panel is painted with a series of very narrow vertical 
    stripes, consisting of red, green and blue phosphors. These stripes are 
    separated by a narrow black graphite stripe guard band. When struck by an 
    electron beam, the phosphors will illuminate, but the graphite will not. This 
    prevents colour impurity by ensuring that the electron beam only strikes 
    the phosphor stripes it is intended to light.
     
    The electron beam is generated by the electron gun assembly, which houses 
    three electron guns situated side-by-side. Each of the three guns emits an 
    electron beam (also called a cathode ray) into the tube, through the mask 

    and onto the panel.


    Because the three beams travel side-by-side, the holes in the mask ensure 
    that each beam, because of its different angle of attack, will hit only a 
    specific phosphor stripe; red, green or blue. The three phosphors, lighted 
    in different combinations of intensity, can create any visible colour when 
    viewed from even a slight distance.

     The three electron beams are directed across the screen through a series of 
    electromagnets, called a yoke, which draw the beams horizontally across 
    the screen in line at a time. Depending on the screen size, the beam draws 
    about 500 lines across the entire screen. Each time, the phosphors light up 
    to produce an image.

    The electron guns and the yoke are electronically synchronized to ensure 
    the lines of phosphors are lighted properly to produce an accurate image. The 
    image lasts only for about a 1/30th of a second. For that reason, the picture 
    must be redrawn 30 times in a second. The succession of so many pictures 

    produces the illusion of movement, just like the frames on movie film.

    9.7 FLUORESCENCE AND PHOSPHORESCENCE
     Fluorescence is the emission of light by a substance that has absorbed light 
    or other electromagnetic radiation. It is a form of photoluminescence. 
    In most cases, the emitted light has a longer wavelength, and therefore, 
    lower energy than the absorbed radiation. However, when the absorbed 
    electromagnetic radiation is intense, it is possible for one electron to absorb 
    two photons; this two-photon absorption can lead to emission of radiation 
    having a shorter wavelength than the absorbed radiation. The emitted 
    radiation may also be of the same wavelength as the absorbed radiation, 
    termed “resonance fluorescence”.
     Fluorescence occurs when an orbital electron of a molecule or atom relaxes 
    to its ground state by emitting a photon of light after being excited to a 
    higher quantum state by some type of energy. The most striking examples 
    of fluorescence occur when the absorbed radiation is in the ultraviolet region 
    of the spectrum, and thus invisible to the human eye, and the emitted light 
    is in the visible region.

     Phosphorescence is a specific type of photoluminescence related to 
    fluorescence. Unlike fluorescence, a phosphorescent material does not 
    immediately re-emit the radiation it absorbs. Excitation of electrons to 
    a higher state is accompanied with the change of a spin state. Once in a 
    different spin state, electrons cannot relax into the ground state quickly 
    because the re-emission involves quantum mechanically forbidden energy 
    state transitions. As these transitions occur very slowly in certain materials, 
    absorbed radiation may be re-emitted at a lower intensity for up to several 

    hours after the original excitation.


    9.8 PHOTOELECTRIC EMISSION LAWS 
    Law 1:
     The photocurrent is directly proportional to the intensity of light and is 
    independent of frequency. 

    Explanation
     According to quantum theory, each photon interacts only with each 
    electron. When the intensity is increased more photons will come and they 
    will interact with more electrons. This will increase the amount of photo 
    current.
     
    Law 2:
     The kinetic energy of the photoelectrons is directly proportional to frequency 
    and is independent of intensity.
     
    Explanation
     According to Einstein’s equation, hf0 is constant. Then kinetic energy is 
    directly proportional to frequency.
     
    Law 3:
     Photoelectric effect does not happen when the incident frequency is less 
    than a minimum frequency (threshold frequency). 

    Explanation 
    From Einstein’s equation, if , then kinetic energy becomes negative 
    and it is impossible, in other words photoelectric effect does not happen.
     
    Law 4:
     There is no time lag between the incidence of photon and emission of 
    electrons. Thus, photoelectric process is instantaneous. 

    Explanation
     According to quantum theory, each photon interacts with each electron. 
    So different electrons will interact with different photons at same instant. 

    Thus there is no time lag between incidence and emission. 

    9.9 PHOTOELECTRIC EFFECT 
    The photoelectric effect is the emission of electrons from the surface of a 
    metal when electromagnetic radiation (such as visible or ultraviolet light) 
    shines on the metal. At the time of its discovery, the classical wave model 
    for light predicted that the energy of the emitted electrons will increase as 
    the intensity (brightness) of the light increased. It was discovered that it 
    did not behave that way. Instead of using the wave model, treating light 
    as a particle (photon) led to a more consistent explanation of the observed 
    behaviour.

     From photon theory, we note that in a monochromatic beam, all photons 
    have the same energy (equal to hf). Increasing the intensity of the light 
    beam means increasing the number of photons in the beam but does not 
    affect the energy of each photon as long as the frequency is not changed. 
    From this consideration and suggestions of Einstein, the photon theory 
    makes the following predictions:
     1. For a given metal and frequency of incident radiation, the number 
    of photoelectrons ejected per second is directly proportional to the 
    intensity of the incident light.
     2. For a given metal, there exists a certain minimum frequency (f0 ) of 
    incident radiation below which no emission of photoelectrons takes 
    place. This frequency is called the threshold frequency or cutoff 
    frequency.
     3. Above the threshold frequency, the maximum kinetic energy of 
    the emitted photoelectron     is independent of the intensity of the 
    incident light but depends only upon the frequency (or wavelength) of 
    the incident light.
     4. The time lag between the incidence of radiation and the emission of a 
    photoelectron is very small (less than 10-9 second).

     This is evidence of the particle nature of light. 

    9.10  FACTORS AFFECTING PHOTOELECTRIC 

    EMISSION

    Photoelectric current is produced as a result of photoelectric effect. Therefore, 
    understanding the factors which influence the photoelectric effect is very 
    important. The previous studies on photoelectric effect have presented the 
    following factors which may have a direct impact on photoelectric effect. 

    Intensity of Light:
     If a highly intense light of frequency equal to or greater than threshold 
    frequency falls on the surface of matter, the photoelectric effect is caused. 
    Studying the impact of this factor is the focus of this research study. One 
    thing which is very clear is that the emission of electrons does not depend 
    upon the intensity of light unless the frequency of light is greater than the 

    threshold frequency. The threshold frequency varies from matter to matter. 

    Number of Photoelectrons:
     The increase in intensity of light increases the number of photoelectrons, 
    provided the frequency is greater than threshold frequency. In short, the 

    number of photoelectrons increases the photoelectric current. 

    Kinetic Energy of Photoelectrons:
     The kinetic energy of photoelectrons increases when light of high energy 
    falls on the surface of matter. When energy of light is equal to threshold 
    energy, then electrons are emitted from the surface, whereas when energy 
    is greater than threshold energy, then photoelectric current is produced. 
    The threshold frequency is not same for all kinds of matter and it varies 

    from matter to matter. 

    9.11  PHOTON, WORK FUNCTION AND PLANCK'S 
    CONSTANT 
    The photon is the fundamental particle of visible light. In some ways, 
    visible light behaves like a wave phenomenon, but in other respects it acts 
    like a stream of high-speed, submicroscopic particles.
     Minimum amount of energy which is necessary to start photo electric 
    emission is called Work Function. If the amount of energy of incident 
    radiation is less than the work function of metal, no photo electrons are 

    emitted.

    Planck’s constant describes the behaviour of particles and waves on the 
    atomic scale. The idea behind its discovery, that energy can be expressed 
    in discrete units, or quantized, proved fundamental for the development of 

    quantum mechanics. 

    Project 9-1: Photoelectric Effect
    planck introduced the constant (h = 6.63 × 10–34 J.s) in his description of 
    the radiation emitted by a blackbody (a perfect absorber of radiant energy). 
    The constant’s significance, in this context, was that radiation (light, for 
    example) is emitted, transmitted and absorbed in discrete energy packets.
     
    Aim: this project aims at gaining the deep knowledge on photoelectric 
    effect.
     
    Question: Describe the observations made of the photoelectric effect and 
    how this supports the particle model and wave model of light studied in 

    unit 1.
     Hypothesis: write a hypothesis on the phenomenon of photoelectric 
    effect.
     Procedure
       1.  State the main principle of photoelectric effect.
       2.  Outline your observations on different conditions
     Collecting Data
     Use internet and textbooks to analyse the phenomenon of photoelectric 
    effect.
     Report design
     Write your report of at least five supporting points including the one 

    given in the format below:



     9.12 EINSTEIN’S EQUATION 
    According to Einstein’s theory, an electron is ejected from the metal by 
    a collision with a single photon. In the process, all the photon energy is 
    transferred to the electron and the photon ceases to exist. Since electrons 
    are held in the metal by attractive forces, a minimum energy (W0 ) is 
    required just to get an electron out through the surface. W0
     is called the 
    work function, and is a few electron volts (1eV = 1.6 × 10–19 J ) for most 

    metals.

    Definitions
     Photoelectric emission is the phenomenon of emission of electrons from 
    the surface of metals when the radiations of suitable frequency and suitable 
    wavelength fall on the surface of the metal.
     Work function is the minimum energy required to set free an electron 
    from the binding forces on the metal surface.
     The Threshold Frequency is defined as the minimum frequency of 
    incident light required for the photoelectric emission.
     If the frequency f  of the incoming light is so low that hf is less than W0
     , then the photons will not have enough energy to eject any electrons at all. If  
    hf > W0, then electrons will be ejected and energy will be conserved in the 
    process. 

    So Einstein suggested that the energy of the incident radiation hf was 
    partly used to free electrons from the binding forces on the metal and the 
    rest of the energy appeared as kinetic energy of the emitted electrons. This 
    is stated in the famous Einstein’s equation of photoelectric effect as stated 

    in equation 9-7 below.


     Equation 9-8 is called the Einstein’s photoelectric equation.
     Many electrons will require more energy than the bare minimum W0
     to get out of the metal, and thus the kinetic energy of such electrons will be less 

    than the maximum.

     Application Activity 9.1

     Match the mathematical symbols and their descriptions


    Stopping potential
     The circuit is exposed to radiations of light of frequency f and the supply of 
    potential difference V is connected as shown in Fig.9-15 below. The cathode 
    C is connected at the positive terminal of the supply and the anode P is 

    connected on the negative terminal of the supply.


     If the circuit is exposed to radiations with the battery reversed as shown in 
    Fig. 9-16, current reduces due to the fact that all electrons emitted are not 
    able to reach the anode P. If this potential difference is increased until no 
    electron reaches the anode P, no current flows and this applied potential is 

    called a stopping potential.



    EXAMPLE 9-1
     The work function for lithium is 4.6 × 10-19 J.
     (a) Calculate the lowest frequency of light that will cause photoelectric 
    emission.
     (b) What is the maximum energy of the electrons emitted when the light of  

    frequency 7.3 × 1014 Hz is used? 


    EXAMPLE 9-2
     Selenium has a work function of 5.11 eV. What frequency of light would just 
    eject electrons? 

    Solution:
     When electrons are just ejected from the surface, their kinetic energy is zero.

     So,  


    Application Activity 9.2
     1. Complete table 1 below.
     Table 1: Applying Einstein’s photoelectric equation in 

    calculations


     2. The stopping potential when a frequency of 1.61 × 1015 Hz is 
    incident on a metal is 3 V.
     (a) What is energy transferred by each photon?
     (b) Calculate the work function of the metal.
     (c) What is the maximum speed of the ejected electrons?
     
    Aim: To know the concepts and use of photoelectric equation.
     3.  It is useful to observe the photoelectric effect equation represented 
    graphically. 
    (a) Express equation 9-7 in the form y = a + b, hence or otherwise, 
    explain how Planck’s constant can be calculated from the, graph.
     (b) Express equation 9-8 in the form y = ax + b, hence or otherwise 
    explain how Planck’s constant can be calculated from the graph.

         Aim: To graphically analyse the use of photoelectric equation.
     4.  In an experiment to measure the Planck’s constant, a light emitting 
    diode (LED) was used. Fig. 1-6 was plotted for varying energy of 
    the photon and frequency of the diode. Use the graph to answer the 

    questions that follow.


     (a) Determine the slope of the line.
     (b) What are the intercepts of the graph?
     (c) Write down the equation of the line.
     (d) What do you think is the vertical intercept?
     (e) What is the value of the Planck’s constant?
     (f) Write the Einstein photoelectric equation in relation to the answer  

    of (e)

    9.13 APPLICATION OF PHOTOELECTRIC EFFECT 
    (PHOTO EMISSIVE AND PHOTOVOLTAIC CELLS)
     a) Photo electric cell
     Photoelectric effect is applied in photoelectric cells or simply photocells. 
    These cells change light energy into electric current. Photoelectric cell 
    makes use of photoelectric effect and hence converts light energy into 
    electrical energy. The strength of the current depends on the intensity of 
    light falling on the cathode.

     A photocell consists of an evacuated tube which is transparent to radiations 
    falling on it. It contains two electrodes; a semi-cylindrical cathode coated 
    with photosensitive material and an anode consisting of a straight wire or 

    loop.


    When radiations fall on the cathode, photoelectrons are emitted which are 
    collected by the anode if it is positive with respect to the cathode. They, 
    then, go through the external circuit causing electric current. As intensity 
    of radiations increases, the number of electrons emitted by photoelectric 
    effect also increases. Hence current also increases.
     An everyday example is a solar powered calculator and a more exotic 

    application would be solar panels and others. 


    b) Automatic door opener
     • Automatic doors operate with the help of sensors. Sensors do exactly 
    what they sound like they would do:
     They sense things. There are many different types of sensors that can 

    sense different types of things, such as sound, light, weight, and motion.

    c) Smoke detectors
     • Photoelectric Smoke Detectors. A photoelectric smoke detector is 
    characterized by its use of light to detect fire. The alarm detects smoke; 
    when smoke enters the chamber, it deflects the  light-emitting diode light 
    from the straight path into a photo sensor in a different compartment in 

    the same chamber.

     d) Remote control
     • An Infra-Red (IR) remote (also called a transmitter) uses light to carry 
    signals from the remote to the device it controls. It emits pulses of 
    invisible infrared light that correspond to specific binary codes. Radio

    frequency remotes work in a similar way.

    9.14 COMPTON EFFECT
     Convincing evidence that light is made up of particles (photons) and photons 
    have momentum can be seen when a photon with high energy hf collides 
    with a stationary electron.
     Compton effect says that when x-rays are projected on the target, they 
    are scattered after hitting the target and change the direction they were 
    moving. This means that as a photon interacts with a free electron, the 
    process of photon absorption is forbidden by conservation laws, but the 
    photon scattering may occur. If the electron was originally at rest, then, as 
    a result of interaction, it acquires a certain velocity.
     The energy conservation laws require that the photon energy decreases by 
    the value of the electron kinetic energy, which means that its frequency 
    must also decrease. At the same time, from the viewpoint of the wave 
    theory, the frequency of scattered light must coincide with the frequency of 

    incident light.


    The photon scattering on an electron can be considered as an elastic collision 

    of two particles obeying the energy and momentum conservation laws

    END OF UNIT ASSESSMENT
     1. Describe briefly the two conflicting theories of the structure of the atom.
     2. Why was the nuclear model of Rutherford accepted as correct?
     3. What would have happened if neutrons had been used in Rutherford’s 
    experiment? Explain your answer.
     4. What would have happened if aluminium had been used instead of gold 
    in the alpha scattering experiment? Explain your answer.
     5. What three properties of the nucleus can be deduced from the Rutherford 
    scattering experiment? Explain your answer.
     6. Monochromatic light of wavelength 560 nm incident on a metal 
    surface in a vacuum photocell causes a current through the cell due to 
    photoelectric emission from the metal cathode. The emission is stopped 
    by applying a positive potential of 1.30 V to the cathode with respect to 
    the anode. Calculate:
     (a) the work function of the metal cathode in electron volts.
     (b)  the maximum kinetic energy of the emitted photoelectrons when 
    the cathode is at zero potential.
     7. In a Compton scattering experiment, the wavelength of scattered 
    X-rays for scattering angle of 45 degree is found to be 0.024 angstrom.
     (a) What is the wavelength of the incident photon?
     (b) What is the percentage change in the wavelength on Compton 
    scattering?
     8. You use 0.124-nm x-ray photons in a Compton-scattering experiment. 
    (a) At what angle is the wavelength of the scattered x-rays 1.0% 
    longer than that of the incident x-rays? 
    (b) At what angle is it 0.050% longer?
     9. (a) What is the energy in joules and electron volts of a photon of 420
    nm violet light?
     (b) What is the maximum kinetic energy of electrons ejected from 
    calcium by 420-nm violet light, given that the binding energy (or 
    work function) of electrons for calcium metal is 2.71 eV?
     10. An electron and a positron, initially far apart, move towards each other 
    with the same speed. They collide head-on, annihilating each other and 
    producing two photons. Find the energies, wavelengths and frequencies 
    of the photons if the initial kinetic energies of the electron and positron are
     (a) both negligible and 
    (b) both 5.000 MeV. The electron rest energy is 0.511 MeV.
     11. (a) Calculate the momentum of a visible photon that has a wavelength 
    of 500 nm. 
    (b) Find the velocity of an electron having the same momentum. 
    (c) What is the energy of the electron, and how does it compare with 
    the energy of the photon?
     12. For an electron having a de Broglie wavelength of 0.167 nm (appropriate 
    for interacting with crystal lattice structures that are about this size): 
    (a) Calculate the electron’s velocity, assuming it is non-relativistic. 
    (b) Calculate the electron’s kinetic energy in eV.
     
    UNIT SUMMARY
     Structure of atom
     An atom is a sphere in which positively charged particles called protons and 
    negatively charged particles called electrons are embedded. 

    Rutherford’s atomic model 
    Rutherford performed experiments by the scattering of alpha particles on 
    extremely thin gold foils. From these experiments, a new model of the atom 
    called Rutherford’s planetary model of the atom was born. The following 
    conclusions were made as regard as atomic structure:
     • Most of the mass and all of the charge of an atom concentrated in a 
    very small region which is called atomic nucleus.
     • Nucleus is positively charged and its size is of the order of 10–15 m ≈ 1 
    Fermi.
     • In an atom, there is maximum empty space and the electrons revolve around 
    the nucleus in the same way as the planets revolve around the sun.
     
    Bohr’s atomic model
     Bohr’s model is based on the following postulates: 
    • Each electron moves in a circular orbit centered at the nucleus.
     • The centripetal force needed to the electron moving in a circle is 
    provided by electrostatic force of attraction between the nucleus and 
    electrons.
    • The angular momenta of electrons are whole number multiples of

    • When electron moves in its allowed orbit, it doesn’t radiate energy. 
    The atom is then stable, such stable orbits are called stationary orbits.
     • When an electron jumps from one allowed orbit to another it radiates 
    energy. The energy of radiation equals energy difference between levels.
     hf = Ei – Ef
     Energy levels and spectral lines of Hydrogen
     When hydrogen atom is excited, it returns to its normal unexcited (or ground 
    state) state by emitting the energy it had absorbed earlier. Transition from 
    different orbits cause different wavelengths. These constitute spectral 
    series which are characteristic of the atom emitting them. 
    The spectral lines arising from the transition of electron forms a spectra 
    series. Mainly there are five series and each series is named after its 
    discover as Lyman series, Balmer series, Paschen series, Brackett series 
    and Pfund series. 

    Thermionic emission 
    Thermionic emission or discharge of electrons from heated materials, is 
    widely used as a source of electrons in conventional electron tubes (e.g., 
    television picture tubes) in the fields of electronics and communications. 
    Applications of cathode rays
     • Cathode ray oscilloscope
     • TV tubes
     
    Fluorescence and phosphorescence
     Fluorescence is the emission of light by a substance that has absorbed light 
    or other electromagnetic radiation. 
    Phosphorescence is a specific type of photoluminescence related to 
    fluorescence. Unlike fluorescence, a phosphorescent material does not 
    immediately re-emit the radiation it absorbs. 

    Photoelectric emission laws’
     Law 1: The photo current is directly proportional to the intensity of light 
    and is independent of frequency. 
    Law 2: The kinetic energy of the photo electrons is directly proportional to 
    frequency and is independent of intensity.
     Law 3: Photoelectric effect does not happen when the incident frequency is 
    less than a minimum frequency (threshold frequency). 
    Law 4: There is no time lag between the incidence of photon and emission 
    of electrons.
     
    Photoelectric effect 
    The photoelectric effect is the emission of electrons from the surface of a 
    metal when electromagnetic radiation (such as visible or ultraviolet light) 
    shines on the metal. 

    Factors affecting photoelectric emission 
    • Intensity of Light:
     • Frequency:
     • Number of Photoelectrons
     • Kinetic Energy of Photoelectrons
     Einstein’s equation photoelectric effect 
    Einstein suggested that the energy of the incident radiation hf was partly 
    used to free electrons from the binding forces on the metal and the rest 
    of the energy appeared as kinetic energy of the emitted electrons and his 
    famous equation is;
    
     If the reverse potential difference applied on the circuit is increased until 
    no electron reaches the anode, no current flows and this applied potential 
    is called a stopping potential. This changes the Einstein’s photoelectric 

    equation to;


    Application of photoelectric effect

    Photoelectric effect is applied in photoelectric cells or simply photocells. 
    These cells change light energy into electric current. Photoelectric cell 
    makes use of photoelectric effect and hence converts light energy into 
    electrical energy. The strength of the current depends on the intensity of 

    light falling on the cathode.

    Compton effect
     Compton effect says that when x-rays are projected on the target, they 
    are scattered after hitting the target and change the direction they were 
    moving. 

    The Compton equation (or Compton shift) is given by;