# Physics Class 12 NCERT Solutions: Chapter 11 Dual Nature of Radiation and Matter Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Q: 11. Light of wavelength is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is . Find the work function of the material from which the emitter is made.

Wavelength of light produced by the argon laser,

Stopping potential of the photoelectrons,

Planck՚s constant,

Charge on an electron,

Speed of light,

From Einstein՚s photoelectric effect, we have the relation involving the work function of the material of the emitter as:

Therefore, the material with which the emitter is made has the work function of .

Q: 12. Calculate the

(A) Momentum, and

(B) De Broglie wavelength of the electrons accelerated through a potential difference of .

Potential difference,

Planck՚s constant,

Mass of an electron,

Charge on an electron,

(A) At equilibrium, the kinetic energy of each electron is equal to the accelerating potential, i.e.. , we can write the relation for velocity (v) of each electron as:

The momentum of each accelerated electron is given as:

The momentum of each accelerated electron is given as:

Therefore, the momentum of each electron is .

(B) De Broglie wavelength of an electron accelerating through a potential V, is given by the relation:

Therefore, the de Broglie wavelength of each electron is .