A. How does one explain the emission of electrons from a photosensitive surface with the help of Einstein’s photoelectric equation?

B. The work function of the following metals is given: Na = 2.75 eV, K = 2.3 eV, Mo = 4.17eV and Ni = 5.15 eV. Which of these metals will not cause photoelectric emission for radiation of wavelength from a laser source placed 1 m away from these metals? What happens if the laser source is brought nearer and placed 50 cm away?(the wavelength is not given in the question, I have taken it as 3300 A^o)

A) Einstein’s photoelectric equation is based on the following picture of photoelectric effect: -

Photoelectric emission of electron does happen by continuous absorption of energy coming from radiation. Radiation energy is built up of discrete units, called quanta or photons. Each quantum of radiant energy has energy,

E = hv,

Where h is Planck’s constant and v the frequency of light.

In photoelectric effect, an electron absorbs a quantum of energy of radiation. If the electron absorbs this quantum energy which exceeds the minimum energy needed for the electron to escape from the metal surface (work function ), the electron gets emitted with maximum kinetic energy,

K_max = hv –

The electrons which are tightly bound to the nucleus, emerge with kinetic energies less than the maximum value and increasing the intensity light increase only the number of electrons ejected and not the their kinetic energy, rather kinetic energy is determined by the frequency of the incident radiation.

B) Given: -

Work functions of different metals,

Na, = 2.75 eV

K, = 2.3 eV

Mo, = 4.17 eV

Ni, = 5.15 eV

Calculations: -

Each photon has an energy

E = 0.006 × 10^-16 J

Observations: -

For Na,

Photoelectric effect is observed as work function is smaller than incident energy (2.75 < 3.75), if the laser source is brought nearer and placed 50 cm the no. of photoelectrons ejecting will increase as the intensity of radiation is increasing.

For K,

Photoelectric effect is observed as work function is smaller than incident energy (2.2 < 3.75), if the laser source is brought nearer and placed 50 cm away the no.

of photoelectrons ejecting will increase as the intensity of radiation is increasing.

For Mo,

No photoelectric effect is not observed as work function is greater than incident energy (4.17 > 3.75), if the laser source is brought nearer and placed 50 cm away nothing will happen

For Ni,

No photoelectric effect is observed as work function is greater than incident energy (5.15 > 3.75), if the laser source is brought nearer and placed 50 cm away nothing will happen

Conclusion:

Thus Na and k will cause photo electric effect emission while Mo and Ni will not cause