B.Tech sem I Engineering Physics U-IV Chapter 1-ATOMIC PHYSICS

Atomic Physics

• “Classical Physics”:– developed in 15th to 20th century;– provides very successful description of “every day,

ordinary objects”• motion of trains, cars, bullets,….• orbit of moon, planets• how an engine works,..• subfields: mechanics, thermodynamics, electrodynamics,

• Quantum Physics:• developed early 20th century, in response to

shortcomings of classical physics in describing certain phenomena (blackbody radiation, photoelectric effect, emission and absorption spectra…)

• describes “small” objects (e.g. atoms )

Quantum Physics• QP is “weird and counterintuitive”

• “Those who are not shocked when they first come across quantum theory cannot possibly have understood it” (Niles Bohr)

• “Nobody feels perfectly comfortable with it “ (Murray Gell-Mann)

• “I can safely say that nobody understands quantum mechanics” (Richard Feynman) BUT…

• QM is the most successful theory ever developed by humanity underlies our understanding of atoms, molecules, condensed matter, nuclei, elementary particles

• Crucial ingredient in understanding of stars, …

Features of QP

• Quantum physics is basically the recognition that there is less difference between waves and particles than was thought before

• key insights:• light can behave like a particle• particles (e.g. electrons) are indistinguishable• particles can behave like waves (or wave packets)• waves gain or lose energy only in "quantized

amounts“• detection (measurement) of a particle wave will

change suddenly into a new wave• quantum mechanical interference – amplitudes add• QP is intrinsically probabilistic • what you can measure is what you can know

WAVE-PICTURE OF RADIATION—ENERGY FLOW I S CONTI N UOUS

• Radio waves, microwaves, heat waves, light waves, UV-rays, x-rays and y-rays belong to the family of electromagnetic waves. All of them are known as radiation.

• Electromagnetic waves consist of varying electric and magnetic fields traveling at the velocity of 'c'. The propagation of electromagnetic waves and their interaction with matter can be explained with the help of Maxwell's electromagnetic theory.

• Maxwell's theory treated the emission of radiation by a source as a continuous process.

• A heated body may be assumed to be capable of giving out energy that travels in the form of waves of all possible wavelengths.

• In the same way, the radiation incident on a body was thought to be absorbed at all possible wavelengths.

• The intensity of radiation is given by,

I = 1E12

where E is the amplitude of the electromagnetic wave.

• The phenomena of interference, diffraction and polarization of electromagnetic radiation proved the wave nature of radiation.

• Therefore, it is expected that it would explain the experimental observations made on thermal (heat) radiation emitted by a blackbody.

Blackbody radiation and Planck hypothesis

• Two patches of clouds in physics sky at the beginning of 20th century.

• The speed of light Relativity

• The blackbody radiation foundation of Quantum theory

Blackbody radiation

• Types of heat energy transmission are conduction, convection and radiation.

• Conduction is transfer of heat energy by molecular vibrations not by actual motion of material. For example, if you hold one end of an iron rod and the other end of the rod is put on a flame, you will feel hot some time later. You can say that the heat energy reaches your hand by heat conduction.

• Convection is transfer of heat by actual motion of. The hot-air furnace, the hot-water heating system, and the flow of blood in the body are examples.

• Radiation The heat reaching the earth from the sun cannot be transferred either by conduction or convection since the space between the earth and the sun has no material medium. The energy is carried by electromagnetic waves that do not require a material medium for propagation. The kind of heat transfer is called thermal radiation.

• Blackbody is defined as the body which can absorb all energies that fall on it. It is something like a black hole. No lights or material can get away from it as long as it is trapped. A large cavity with a small hole on its wall can be taken as a blackbody.

• Blackbody radiation: Any radiation that enters the hole is absorbed in the interior of the cavity, and the radiation emitted from the hole is called blackbody radiation.

Fig. 9.1 Blackbody concave.

LAWS OF BLACK BODY RADIATION

1. Stefan and Boltzmann’s law: it is found that the radiation energy is proportional to the fourth power of the associated temperature.

4M(T) T

M(T) is actually the area under each curve, σ is called Stefan’s constant and T is absolute temperature.

2. Wien’s displacement law: the peak of the curve shifts towards longer wavelength as the temperature falls and it satisfies

peakT b

This law is quite useful for measuring the temperature of a blackbody with a very high temperature. You can see the example for how to measure the temperature on the surface of the sun.

where b is called the Wien's constant.b=2.89X10-3

• The above laws describes the blackbody radiation very well.

• The problem exists in the relation between the radiation power Mλ(T) and the wavelength λ.

• Blackbody radiation has nothing to do with both the material used in the blackbody concave wall and the shape of the concave wall.

• Two typical theoretical formulas for blackbody radiation : One is given by Rayleigh and Jeans and the other by Wein.

3.Rayleigh and Jeans

In 1890, Rayleigh and Jeans obtained a formula using the classical electromagnetic (Maxwell) theory and the classical equipartition theorem of energy in thermotics. The formula is given by

2

3

8 kTE( )

c

Rayleigh-Jeans formula was correct for very long wavelength in the far infrared but hopelessly wrong in the visible light and ultraviolet region. Maxwell’s electromagnetic theory and thermodynamics are known as correct theory. The failure in explaining blackbody radiation puzzled physicists! It was regarded as ultraviolet Catastrophe (disaster).

4. Planck Radiation Law:

hcE h

Quantum energy

Planck constant

Frequency

34

15

h 6.626 10 J s

4.136 10 eV s

19

18

1eV 1.602 10 J

1J 6.242 10 eV

PLANCK'S QUANTUM HYPOTHESIS — Energy is quantized

• Max Planck empirical formula explained the experimental observations.

• In the process of formulation of the formula, he assumed that the atoms of the walls of the blackbody behave like small harmonic oscillators, each having a characteristic frequency of vibration, lie further made two radical assumptions about the atomic oscillators.

• (i) An oscillating atom can absorb or mends energy in discrete units. The indivisible discrete unit of energy hs, is the smallest amount of energy which can be absorbed or emitted by the atom and is called an energy quantum. A quantum of energy has the magnitude given by

E = hv

where v is the frequency of radiation and ‘h' is a constant now known as the Planck's constant.

• (ii) The energy of the oscillator is quantized. It can have only certain discrete amounts of energy En.

En= nhv n=1,2,3……

• The hypothesis that radiant energy is emitted or absorbed basically in a discontinuous summer and in the form of quanta is known as the Planck's quantum hypothesis.

• Planck's hypothesis states that radiant energy Is quantized and implies that an atom exists in certain discrete energy states. Such states arc called quantum stales and n is called the quantum number.

• The atom emits or absorbs energy by jumping from one quantum state to another quantum state. The assumption of discrete energy states for an atomic oscillator (Fig.a) was a departure from the classical physics and our everyday experience.

• If we take a mass-spring harmonic oscillator, it can receive any amount of energy form zero to some maximum value (Fig.b). Thus, in the realm of classical physics energy always appears to occur with continuous values and energy exchange between bodies involves any arbitrary amounts of energy.

PARTICLE PICTURE OF RADIATION —Radiation is a stream of photons

• Max Planck introduced the concept of discontinuous emission and absorption of radiation by bodies but he treated the propagation through space as occurring in the form of continuous waves as demanded by electromagnetic theory.

• Einstein refined the Planck's hypothesis and invested the quantum with a clear and distinct identity.

• He successfully explained the experimental results of the photoelectric effect in 1905 and the temperature dependence of specific heats of solids in 1907 basing on Planck's hypothesis.

• The photoelectric effect conclusively established that light behaves as a swam of particles. Einstein extended Planck's hypothesis as follows:

1. Einstein assumed that the light energy is not distributed evenly over the whole expanding wave front but rather remains concentrated in discrete quanta. He named the energy quanta as photons. Accordingly, a light beam is regarded as a stream of photons travelling with a velocity ' c' .

2. An electromagnetic wave having a frequency f contains identical photons, each having an energy hƒ. The higher the frequency of the electromagnetic wave, the higher is the energy content of each photon.

3. An electromagnetic wave would have energy hƒ if it contains only one photon. 2hv if it contains 2 photons and so on. Therefore, the intensity of a monochromatic light beam I. is related to the concentration of photons. N. present in the beam. Thus,

I = N hƒ

Note that according to electromagnetic theory, the intensity of a light beam is given by

I = 1E12

4. When photons encounter matter, they impart all their energy to the panicles of matter and vanish. That is why absorption of radiation is discontinuous. The number of photons emitted by even a weak light source is enormously large and the human eye cannot register the photons separately and therefore light appears as a continuous stream. Thus, the discreteness of light is not readily apparent.

The Photon • As the radiant energy is viewed as made up of

spatially localized photons. we may attribute particle properties to photons.

1. Energy: The energy of a photon is determined by its frequency v and is given by E = hƒ. Using the relation ω= 2π ט and writing h/2π = ħ. we may express E= ħω

2. Velocity: Photons always travel with the velocity of light ‘c'.

3. Rest Mass: The rest mass of photon is zero since a photon can never be at rest. Thus, m0= 0

4. Relativistic mass: As photon travels with the velocity of light, it has relativistic mass. given by m= E/c2 = hv/c2

The Photon • As the radiant energy is viewed as made up of

spatially localized photons. we may attribute particle properties to photons.

1. Energy: The energy of a photon is determined by its frequency v and is given by E = hƒ. Using the relation ω= 2π ט and writing h/2π = ħ. we may express

E= ħω

2. Velocity: Photons always travel with the velocity of light ‘c'.

3. Rest Mass: The rest mass of photon is zero since a photon can never be at rest. Thus, m0= 0

4. Relativistic mass: As photon travels with the velocity of light, it has relativistic mass. given by m= E/c2 = hv/c2

5. Linear Momentum: The linear momentum associated with a photon may be expressed as p=E/c=hv/c= h/λ

As the wave vector k= 2π/λ , p = hk/ 2π = ħk.

6. Angular Momentum: Angular momentum is also known as spin which is the intrinsic property of all microparticles. Photon has a spin of one unit. Thus. s = lħ.

7. Electrical Charge: Photons are electrically neutral and cannot be influenced by electric or magnetic fields. They cannot ionize matter.

Example: Calculate the photon energies for the following types of electromagnetic radiation: (a) a 600kHz radio wave; (b) the 500nm (wavelength of) green light; (c) a 0.1 nm (wavelength of) X-rays.

Solution: (a) for the radio wave, we can use the Planck-Einstein law directly

15 3

9

E h 4.136 10 eV s 600 10 Hz

2.48 10 eV

(b) The light wave is specified by wavelength, we can use the law explained in wavelength:

6

9

hc 1.241 10 eV mE 2.26eV

550 10 m

(c). For X-rays, we have

64

9

hc 1.241 10 eV mE 1.24 10 eV 12.4keV

0.1 10 m

Photoelectric Effect

The quantum nature of light had its origin in the theory of thermal radiation and was strongly reinforced by the discovery of the photoelectric effect.

Fig. Apparatus to investigate the photoelectric effect that was first found in 1887 by Hertz.

Photoelectric Effect

In figure , a glass tube contains two electrodes of the same material, one of which is irradiated by light. The electrodes are connected to a battery and a sensitive current detector measures the current flow between them.

The current flow is a direct measure of the rate of emission of electrons from the irradiated electrode.

The electrons in the electrodes can be ejected by light and have a certain amount of kinetic energy. Now we change:

(1) the frequency and intensity of light,

(2) the electromotive force (e.m.f. or voltage),

(3) the nature of electrode surface.

It is found that:

(1). For a given electrode material, no photoemission exists at all below a certain frequency of the incident light. When the frequency increases, the emission begins at a certain frequency. The frequency is called threshold frequency of the material. The threshold frequency has to be measured in the existence of e.m.f. (electromotive force) as at such a case the photoelectrons have no kinetic energy to move from the cathode to anode . Different electrode material has different threshold frequency.

(2). The rate of electron emission is directly proportional to the intensity of the incident light.

Photoelectric current The intensity of light ∝

(3). Increasing the intensity of the incident light does not increase the kinetic energy of the photoelectrons.

Intensity of light kinetic energy of photoelectron ∝

However increasing the frequency of light does increase the kinetic energy of photoelectrons even for very low intensity levels.

Frequency of light kinetic energy of photoelectron ∝

(4). There is no measurable time delay between irradiating the electrode and the emission of photoelectrons, even when the light is of very low intensity. As soon as the electrode is irradiated, photoelectrons are ejected.

(5) The photoelectric current is deeply affected by the nature of the electrodes and chemical contamination of their surface.

In 1905, Einstein solved the photoelectric effect problem by applying the Planck’s hypothesis. He pointed out that Planck’s quantization hypothesis applied not only to the emission of radiation by a material object but also to its transmission and its absorption by another material object. The light is not only electromagnetic waves but also a quantum. All the effects of photoelectric emission can be readily explained from the following assumptions:

(1) The photoemission of an electron from a cathode occurs when an electron absorbs a photon of the incident light;

(2) The photon energy is calculated by the Planck’s quantum relationship: E = hν.

(3) The minimum energy is required to release an electron from the surface of the cathode. The minimum energy is the characteristic of the cathode material and the nature of its surface. It is called work function.

Therefore we have the equation of photoelectric effect: 21

2 h A mv

Photon energy

Work functionPhotoelectron kinetic energy

Using this equation and Einstein’s assumption, you could readily explain all the results in the photoelectric effect: why does threshold frequency exist (problem)? why is the number of photoelectrons proportional to the light intensity? why does high intensity not mean high photoelectron energy (problem)? why is there no time delay (problem)?

Example: Ultraviolet light of wavelength 150nm falls on a chromium electrode. Calculate the maximum kinetic energy and the corresponding velocity of the photoelectrons (the work function of chromium is 4.37eV).

Solution: using the equation of the photoelectric effect, it is convenient to express the energy in electron volts. The photon energy is

6

9

1.241 108.27

150 10

hc eV m

E h eVm

and

2

2

1

21

(8.27 4.37) 3.902

h A mv

mv eV eV

19 19 19 2 21 1.602 10 1.602 10 1.602 10 eV J N m kg m s

∴ 2 19 2 213.90 3.90 1.602 10

2 mv eV kg m s

∴19

631

2 3.90 12.496 101.17 10 /

9.11 10

eV

v m sm

Examples

1. The wavelength of yellow light is 5890 A. What is the energy of the photons in the beam? Empress in electron volts.

2. 77w light sensitive compound on most photographic films is silver bromide, Aglin A film is exposed when the light energy absorbed dissociates this molecule into its atoms. The energy of dissociation of Agllr is 23.9 k.catitnot Find the energy in electron volts, the wavelength and the frequency of the photon that is just able to dissociate a molecule of silver bromide.

3. Calculate the energy of a photon of blue light with a frequency of 6.67 x 1014 Hz. (State in eV) [2.76eV]

4. Calculate the energy of a photon of red light with a wavelength of 630 nm. [1.97eV]

5. Barium has a work function of 2.48 eV. What is the maximum kinetic energy of the ejected electron if the metal is illuminated by light of wavelength 450 nm? [0.28 eV]

6. When a 350nm light ray falls on a metal, the maximum kinetic energy of the photoelectron is 1.20eV. What is the work function of the metal? [2.3 eV]

7. A photon has 3.3 x 10-19 J of energy. What is the wavelength of this photon?

8. What is the energy of one quantum of 5.0 x 1014 Hz light?