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 $589nm$ .
(i) What is the energy per photon associated with the sodium light?
(ii) At what rate are the photons delivered to the sphere?

• A. (i) 4.6 eV (ii) $1.6\times 10^{24}$ photon/s
• B. (i) 3.4 eV (ii) $4.5\times 10^{24}$ photon/s
• C. (i) 2.1 eV (ii) $3\times 10^{20}$ photon/s
• D. (i) 1.1 eV (ii) $2\times 10^{24}$ photon/s

Answer 1

Answer: (C)

Given, power of lamp, $P=100W$
Wavelength of the sodium light, $\lambda =589nm=589\times 10^{-9}m$
Planck constant $h=6.63\times 10^{-34}J-s$
(i) Energy of each photon
$E=\frac{hc}{\lambda }=\frac{6.63\times 10^{-34}\times 3\times 10^8}{589\times 10^{-9}}\left(\because c=3\times 10^{8}m/s\right)$
$=3.38\times 10^{-19}J$
$=\frac{3.38\times 10^{-19}}{1.6\times 10^{-19}}eV$
$=2.11eV$
(ii) Let $n$ photons are delivered per second.
$\therefore n=\frac{\text{ Power }}{\text{ Energy of each photon }}(\text{ From }P=En)$
$=\frac{100}{3.38\times 10^{-19}}=3\times 10^{20}$ photon/s
$=3\times 10^{20}$ photon / s are delivered