Physics Class 12 NCERT Solutions: Chapter 11 Dual Nature of Radiation and Matter Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Photoelectric Effect Equation

Q: 7. A sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is . (A) What is the energy per photon associated with the sodium light? (B) At what rate are the photons delivered to the sphere?

Answer:

Power of the sodium lamp,

Wavelength of the emitted sodium light,

Planck՚s constant,

Speed of light,

(A) The energy per photon associated with the sodium light is given as:

(B) Number of photons delivered to the sphere

The equation for power can be written as:

Therefore, every second, photons are delivered to the sphere.

Q: 8. The threshold frequency for a certain metal is . If light of frequency is incident on the metal, predict the cutoff voltage for the photoelectric emission.

Answer:

Threshold frequency of the metal,

Frequency of light incident on the metal,

Charge on an electron,

Planck՚s constant,

Cut-off voltage for the photoelectric emission from the metal

The equation for the cut-off energy is given as:

Therefore, the cut-off voltage for the photoelectric emission is

Q: 9. The work function for a certain metal is . Will this metal give photoelectric emission for incident radiation of wavelength ?

Answer:

No

Work function of the metal,

Charge on an electron,

Planck՚s constant,

Wavelength of the incident radiation,

Speed of light,

The energy of the incident photon is given as:

It can be observed that the energy of the incident radiation is less than the work function of the metal. Hence, no photoelectric emission will take place.

Q: 10. Light of frequency is incident on a metal surface. Electrons with a maximum speed of are ejected from the surface. What is the threshold frequency for photoemission of electrons?

Answer:

Frequency of the incident photon,

Maximum speed of the electrons,

Planck՚s constant,

Mass of an electron,

For threshold frequency, the relation for kinetic energy is written as:

Therefore, the threshold frequency for the photoemission of electrons is

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