Question

A 100 W 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. At what rate are the photons from the lamp associated with the sodium light

Answer 1

The rate at which photons from the lamp are associated with the sodium light is 2.96×$10^{20}$.

Power of the sodium lamp, P=100 W

The wavelength of the emitted sodium light, λ=589 nm = 589×$10^{-9}$m

Planck's constant, h=6.626×$10^{-34}$Js

Speed of light, c= 3×$10^{8}$m/s

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

E =hcλ

E =6.626×$10^{-34}$×3×108/589×$10^{-9}$=3.37×$10^{-19}$J

E =$\frac{3.37*10^{-19} }{1.6*10^{-19} }$=2.11eV

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

The equation for power can be written as P=nE

∴n =PE

=1003.37×$10^{-19}$ =2.96×$10^{20}$photons/s

Therefore, every second, 2.96×$10^{20}$ photons are delivered to the sphere.

To know more about photons refer to: brainly.com/question/26412768

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