Physics Class 12 NCERT Solutions: Chapter 11 Dual Nature of Radiation and Matter Part 2

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Energy of a single photon

Energy of a Single Photon

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Q: 4. Monochromatic light of wavelength is produced by a helium-neon laser. The power emitted is.

(A) Find the energy and momentum of each photon in the light beam,

(B) How many photons per second, on the average, arrive at a target irradiated by this beam? (Assume the beam to have uniform cross-section which is less than the target area), and

(C) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?

Answer:

Wavelength of the monochromatic

Power emitted by the laser,

Planck’s constant,

Speed of light,

Mass of a hydrogen atom,

(A)The energy of each photon is given as:

The momentum of each photon is given as:

(B)Number of photons arriving per second, at a target irradiated by the beam Assume that the beam has a uniform cross-section that is less than the target area.

Hence, the equation for power can be written as:

(C)Momentum of the hydrogen atom is the same as the momentum of the photon,

Momentum is given as:

Where,

Speed of the hydrogen atom

Q: 5. The energy flux of sunlight reaching the surface of the earth is. How many photons (nearly) per square metre are incident on the Earth per second? Assume that the photons in the sunlight have an average wavelength of.

Answer:

Energy flux of sunlight reaching the surface of earth,

Hence, power of sunlight per square metre,

Speed of light,

Planck’s constant,

Average wavelength of photons present in sunlight,

Number of photons per square metre incident on earth per second

Hence, the equation for power can be written as:

Therefore, every second, photons are incident per square meter on earth.

Q: 6. In an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of incident light is found to be V s. Calculate the value of Planck’s constant.

Answer:

The slope of the cut-off voltage versus frequency of an incident light is given as:

is related to frequency by the equation:

Where,

Charge on an electron

Planck’s constant

Therefore, the value of Planck’s constant is