Q. A $100 \, \text{W}$ sodium lamp radiates energy uniformly in all directions. The wavelength of the sodium light is $589 \text{ nm}$ . What is the energy per photon in $\left(\right.eV\left.\right)$ associated with the sodium light? [ $\text{h = 6} \text{.63 \times 10}^{\text{-34}} \text{ J s}$ ]

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A

$\text{2} \text{.11}$

B

$\text{1.22}$

C

$\text{0.5}$

D

$\text{3.21}$

Solution:

Given, power of the lamp, $\text{P = 100 W}$
The wavelength of the sodium light, $\lambda = 5 8 9$ $\text{nm = 589 } \times \text{ 10}^{- 9} \text{ m}$
Planck constant $h=6.63 \times 10^{-34} J s$
The energy of each photon
$\textit{E}=\frac{\textit{hc}}{\lambda }=\frac{6 \text{.} 6 3 \times 1 0^{- 3 4} \times 3 \times 1 0^{8}}{5 8 9 \times 1 0^{- 9}}$
$\left(\because \text{c} = 3 \times 1 0^{8} \left(\text{ m s}\right)^{- 1}\right)$
$= 3 \text{.} 3 8 \times 1 0^{- 1 9} \text{ J}$
$= \frac{3 \text{.} 3 8 \times 1 0^{- 1 9}}{1 \text{.} 6 \times 1 0^{- 1 9}}$ $eV$
$\text{= 2}\text{.11}$ $eV$

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