Question

Calculate the number of photons emitted per second by a 10 W sodium vapour lamp. Assume that 60% of the consumed energy is converted into light. Wavelength of sodium light = 590 nm

Answer 1

Given:
Power of the sodium vapour lamp, P = 10 W
Wavelength of sodium light, $\lambda$ = 590 nm
Electric energy consumed by the bulb in one second = 10 J
Amount of energy converted into light = 60 %
∴ Energy converted into light = $\frac{60}{100}\times 10=6\mathrm{J}$
Energy needed to emit a photon from the sodium atom,
$$\begin{gathered} E\text{'}=\frac{hc}{\lambda } \\ E\text{'}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{590\times {10}^{-9}} \\ E\text{'}=\frac{6.63\times 3}{590}\times {10}^{-17}\mathrm{J} \end{gathered}$$

Number of photons emitted,
$$\begin{gathered} n=\frac{6}{{\displaystyle \frac{6.63\times 3}{590}}\times {10}^{-17}} \\ n=\frac{6\times 590}{6.63\times 3}\times {10}^{17} \end{gathered}$$
n = 1.77 × 10¹⁹