# 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 him. The $\lambda$ of sodium light is 589 nm. At what rate are the photons delivered to the sphere ?

$\begin {array} {1 1} (a)\;29.6 \times 10^{21} photon/s & \quad (b)\;2.96 \times 10^{20} photon/s \\ (c)\;0.296 \times 10^{20} photon/s & \quad (d)\;2.96 \times 10^{21} photon/s \end {array}$

Ans : (b) $2.96 \times 10^{20} photon/s$
Energy per photon in light, $E = hc/\lambda = ( 6.626 \times 10^{-34} \times 3 \times 10^8) / (589 \times 10^{-9} ) = 3.37 \times 10^{-19}J$
No. of photons delivered to the sphere $= P/E$
$= 100/ ( 3.37 \times 10^{-19} ) = 2.96 \times 10^{20} photon/s$

edited Mar 13, 2014