^Photoelectric effect

1. An instantaneous process (10^-8 s) of emission of free electrons from the surface of a metal (also called cathode) when light photons of energy greater than threshold frequency are incident on it.

2. Einstein experimentally confirmed that the Photoelectric effect is a one-photon-one electron process & verifies the quantum nature of light as it is the result of particle-particle interaction.

3. Threshold energy (or work function) is the least energy required by an electron to come out of the metal. Its value is few eV & it depends only on the nature of metallic surface & impurities present in it & is independent of the energy or incident photons. W = W₀ = E _th = hf _th.

4. Alkali metals like Li, Na, K, Cs, Rb etc. show PEE with visible light. Metals like Zn, Cd, Mn etc. are sensitive only to UV-light. Cs (Cesium) is the best photosensitive metal.

^Einstein’s mass-energy equivalence

The relation

is called relativistic energy or Einstein’s mass-energy equivalence as it reveals that mass & energy are interconvertible.  Here the quantity m₀ c² is the energy associated with the rest mass of the body, K is the kinetic energy of the body & the sum of KE & rest mass energy is called the total energy (E) of the body.

Differentiating this relation we get

c².2 m dm – m².2v dv – v².2m dm = 0

or c² dm = mv.dv + v² dm            _ _ _ _ (1)

Also according to Newton’s second law of motion, force acting on a body is defined as the rate of change of its momentum i.e.

Now if this force F displaces the body by a distance dx, its energy increases by

Equating (1) & (2) we get

dK = dm.c²                                            _ _ _ _ (3)

If particle is accelerated from rest to a velocity v, let its mass m₀ increase to m, then its total increase in KE can be obtained by integrating equation (3) , i.e.

Suppose a body of rest mass m₀ moves with a velocity v << c.  Its mass at speed v is

As mc² is the total energy and m₀ c² is the rest mass energy. Therefore the term (mc² – m₀ c²) represents the kinetic energy, thus KE of the body is

This is the same result that we obtain by classical Newtonian mechanics.

Facts

1. Zero rest mass i.e. m₀ = 0 means massless particle & for such particles, E = pc i.e. even a massless particle can possess energy.

2. An electron and photon have same de-broglie wavelength. Which has more total energy?

Ans. Same λ means same p (as, p = h/λ) & quantity having more m₀ will have more E, i.e. Electron.

3. An electron and proton have same total energy. Which has more de-broglie wavelength?

Ans. In order to have same E the quantity having less m₀ must have more p or less λ (as, p = h/λ), i.e. Electron.

4. Also KE of a particle is

5. If a photon and electron has same de Broglie wavelength, then the KE of the photon is  times the kinetic energy of the electron.

Commonly used values

1. Charge of electrons = e = – 1.6 x 10^-19 C

2. Rest mass of electrons = m₀ = 9.1 x 10^-31

3. Sp. charge of electron = e/m₀ = 1.76 x 10¹¹ C/ kg

4. hc = 1.989 x 10^-25  » 2 x 10^-25

5.

^Electron microscope

The wave properties of electrons have been utilised in the design of electron microscope. Resolving power of an electron microscope is expressed as .

Resolving power of electron microscope can be up to 10⁵ times that of optical microscope.

^Millikan oil-drop experiment

In 1913, Millikan measured the charge on an electron precisely using oil-drop experiment. He found that the charge on an oil-droplet was always an integral multiple of an elementary charge, 1.602 × 10^-19 C. Millikan’s experiment established that electric charge is quantised. From the values of charge (e) and specific charge (e/m), the mass (m) of the electron could be determined.

^Intensity of photons

Intensity of photons is also called power density & is defined as the rate of photons (i.e. number of photons per second) crossing a given area at right angles. Mathematically intensity of photons can be expressed as,

All photons of light of a particular frequency f, or wavelength λ, have the same energy and momentum, whatever the intensity of radiation may be. By increasing the intensity of light of given wavelength, there is only an increase in the number of photons per second crossing a given area, with each photon having the same energy. In other words photon energy is independent of intensity of radiation.