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Question:
A 100W 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 589 nm. (a) What is the energy per photon associatedwith the sodium light? (b) At what rate are the photons delivered to the sphere?
Answer:

Power of the sodium lamp, P= 100 W

Wavelength of the emitted sodium light, image030 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-1= 589 nmimage061 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-1m

Planck’s constant, himage062 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-1 Js

Speed of light, c image063 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-1m/s

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

image064 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-1

image065 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-1

image066 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-1

(b)Number of photons delivered to the sphere = n

The equation for power can be written as:

image050 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-1

image039 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-1

image067 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-1

Therefore, every second, image068 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-1photons are delivered to the sphere.

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