Q1 / 160 · TS EAMCET 2023 (14 May Shift 2) · Chemistry

A 100 watt bulb emits light of wavelength ' $x$ ' $Å$. What is the value of $x$, if the number of photons emitted is $2.0 \times 10^{20} \mathrm{~s}^{-1}$ ? $\left(\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}, 1\right.$ watt $\left.=1 \mathrm{Js}^{-1}\right)$

  • A
    3578
  • B
    4978
  • Correct answer
    C
    3978
  • D
    4578

Solution

Power $=100$ watt $=100 \mathrm{Js}^{-1}$ Number of photons emitted $=2.0 \times 10^{20} \mathrm{~s}^{-1}$ Wavelength $=\mathbf{x}$ Energy of 1 photon $=\frac{h c}{\lambda}$ As, Total Energy $($ Power $)=$ Number of photons emitted $\times$ Energy of 1 photon $\begin{aligned} & 100 \mathrm{~J} \mathrm{~s}^{-1}=2.0 \times 10^{20} \mathrm{~s}^{-1} \times \frac{\mathrm{hc}}{\lambda} \\ & 100 \mathrm{~J} \mathrm{~s}^{-1}=\frac{2.0 \times 10^{20} \mathrm{~s}^{-1} \times 6.63 \times 10^{-34} \mathrm{Js} \times 3 \times 10^8 \mathrm{~ms}^{-1}}{\lambda} \\ & \lambda=\frac{6 \times 6.63 \times 10^{-6} \mathrm{~m}}{100}=39.78 \times 10^{-8} \mathrm{~m}=3978 Å\end{aligned}$

Hence, the correct answer is option: 'C'.

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