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