Question

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 $(eV)$ associated with the sodium light? [ $h=6.63\times 10^{-34}Js$ ]

• A. $\text{2}\text{.11}$
• B. $\text{1.22}$
• C. $\text{0.5}$
• D. $\text{3.21}$

Answer 1

Answer: (A)

Given, power of the lamp, $\text{P = 100 W}$
The wavelength of the sodium light, $\lambda =589$ $\text{nm = 589 }\times {\text{ 10}}^{-9}\text{ m}$
Planck constant $h=6.63\times 10^{-34}Js$
The energy of each photon
$\text{E}=\frac{\text{hc}}{\lambda }=\frac{6\text{.}63\times 10^{-34}\times 3\times 10^8}{589\times 10^{-9}}$
$\left(\because \text{c}=3\times 10^8{\left(\text{ m s}\right)}^{-1}\right)$
$=3\text{.}38\times 10^{-19}\text{ J}$
$=\frac{3\text{.}38\times 10^{-19}}{1\text{.}6\times 10^{-19}}$ $eV$
$\text{= 2}\text{.11}$ $eV$