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Unit 9: ATOMIC MODELS AND PHOTOELECTRIC EFFECT
Unit 9: ATOMIC MODELS AND PHOTOELECTRIC EFFECT
Topic Area: ATOMIC PHYSICS
Sub-Topic Area: QUANTUM PHYSICS
Key unit competence: By the end of this unit I should be able to evaluate the atomic model and photoelectric effect
Unit Objectives:
By the end of this unit learners will be able to;
◊ describe different atomic models by explaining their concepts and drawbacks.
◊ explain the photoelectric effect and its applications in everyday life.
9.0 INTRODUCTION
An atomic theory is a model developed to explain the properties and behaviors 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 ATOM
An atom is a sphere in which positively charged particles called protons and negatively charged particles called electrons are found/embedded. As the number of protons equals the number of electrons, the atom is said to be neutral. This model is called plum pudding model by J.J Thomson. J.J. Thomson gave the first idea regarding structure of atom. According to this model, an atom is a solid sphere in which entire positive charge and it’s mass is uniformly distributed and negative charges (i.e. electron) are embedded like seeds in watermelon.
Success and failure
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;
It was observed that:
• 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
Equation 9-2 is the equation of kinetic energy of a-particle.
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
where h is the Planck’s constant. i.e.
• When electron moves in its allowed orbit, it doesn’t radiate energy. The atom is then stable. Such stable orbits are called stationary orbit.
• When an electron jumps from one allowed orbit to another, it radiates energy. The energy of radiation equals energy difference between levels.
where h is Planck’s constant and f is the frequency of radiation. When electron jumps from higher energy orbit (E1) to lower energy orbit (E2), then difference of energies of these orbits, i.e. E1 – E2 emits in the form of photon. But if electron goes from E2 to E1 it absorbs the same amount of energy.
Notes:
• According to Bohr theory, the momentum of an electron revolving in second orbit of H2 atom will be
• For an electron in the nth orbit of hydrogen atom in Bohr model, circumference of orbit =
= de-Broglie wavelength. Bohr’s Orbits (For Hydrogen and H2-Like Atoms). A: Radius of orbit For an electron around a stationary nucleus, the electrostatics force of attraction provides the necessary centripetal force, i.e. Bohr’s Orbits (For Hydrogen and H2-Like Atoms).
A: Radius of orbit
For an electron around a stationary nucleus, the electrostatics force of attraction provides the necessary centripetal force, i.e.
From equation 9-4 and 9-5, radius of nth orbit
Notes:
• The radius of the innermost orbit (n = 1) of hydrogen atom (z = 1) is called Bohr’s radius a0, i.e. a0 = 0.53. 10-10m
B:Speed of electron
From the above relations, speed of electron in nth orbit can be calculated as
where (c = speed of light 3 × 108 m/s).
Notes:
• The ratio of speed of an electron in ground state in Bohr’s first orbit of hydrogen atom to velocity of light in air is equal to
(where c = speed of light in air).
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 color.
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, Bracket series and Pfund series.
First line of the series is called first member, for which line wavelength is maximum
Last line of the series (n2 = ∞) is called series limit, for which line wavelength is minimum 
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 behavior.
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 behavior 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.
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.
Project 9-1: Photoelectric Effect
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 analyze 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.
ACTIVITY 9-1:Einstein Photoelectric Equation
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.
For this case, the kinetic energy of electrons is given by;
where e is electron charge and Vs is the stopping potential. So, equation 9-7 becomes;
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?
EXERCISE 9-1
1. Complete table 1 below.
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?
9.13 APPLICATION OF PHOTOELECTRIC EFFECT (PHOTO EMISSIVE AND PHOTOVOLTAIC CELLS)
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.
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 collided 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 momentum of the photon can be calculated as follows;
The photon scattering on an electron can be considered as an elastic collision of two particles obeying the energy and momentum conservation laws
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 420nm 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.
13. When a certain photoelectric surface is illuminated with light of different wavelengths, the following stopping potentials are observed:
Plot the stopping potential on the vertical axis against the frequency of the light on the horizontal axis. Determine;
(a) the threshold frequency;
(b) the threshold wavelength;
(c) the photoelectric work function of the material (in electron volts);
(d) the value of Planck’s constant h (assuming that the value of e is known).
14. The human eye is most sensitive to green light of wavelength 505 nm. Experiments have found that when people are kept in a dark room until their eyes adapt to the darkness, a single photon of green light will trigger receptor cells in the rods of the retina.
(a) What is the frequency of this photon?
(b) How much energy (in joules and electron volts) does it deliver to the receptor cells?
(c) To appreciate what a small amount of energy this is, calculate how fast a typical bacterium of mass 9.5 × 10–12 g would move if it had that much energy?
15. The photoelectric work function of potassium is 2.3 eV. If light having a wavelength of 250 nm falls on potassium, find
(a) the stopping potential in volts;
(b) the kinetic energy in electron volts of the most energetic electrons ejected;
(c) the speed of these electrons.
16. Describe the photoelectric effect and discuss why the wave theory of light cannot account for it.
17. Explain how the quantum theory of light accounts for the photoelectric effect.
18. Compare the quantum and wave theories of light and discuss why both are needed.
19. Give the basic ideas of the Bohr model of the atom and show how they follow from the wave nature of moving electrons. 20. Define quantum number, energy level, ground state, and excited state.
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
where h is the Planck number.
• 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;
