A 100 W sodium lamp radiates energy uniformly in all directions.

Power of the sodium lamp, P = 100 W

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 × 108 m/s

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

$E=\frac{h c}{\lambda}$

$=\frac{6.626 \times 10^{-34} \times 3 \times 10^{8}}{589 \times 10^{-9}}=3.37 \times 10^{-19} \mathrm{~J}$

$=\frac{3.37 \times 10^{-19}}{1.6 \times 10^{-19}}=2.11 \mathrm{eV}$

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

The equation for power can be written as:

$P=n E$

$\therefore n=\frac{P}{E}$

$=\frac{100}{3.37 \times 10^{-19}}=2.96 \times 10^{20}$ photons $/ \mathrm{s}$

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