Question

\(10^{20}\) photons of wavelength \(660\,\text{nm}\) are emitted per second from a lamp. The wattage of the lamp is (Planck’s constant \(h=6.6\times10^{-34}\,\text{Js}\))

• A. 30 W
• B. 60 W
• C. 100 W
• D. 500 W

Hint:

Photon power: \begin{itemize} \item Multiply energy per photon by photons/sec. \end{itemize}

Answer 1

The Correct Option is A

Concept: Power = energy emitted per second. Photon energy: \[ E = \frac{hc}{\lambda} \] Step 1: {\color{red}Substitute values.} \[ \lambda = 660\times10^{-9}\text{ m},\quad c=3\times10^8 \] \[ E = \frac{6.6\times10^{-34}\times3\times10^8}{660\times10^{-9}} \] \[ E = 3\times10^{-19}\text{ J} \] Step 2: {\color{red}Total power.} \[ P = 10^{20}\times 3\times10^{-19} = 30\text{ W} \]