With what velocity must an electron travel, so that its momentum is equal to that of a photon of wavelength…
With what velocity must an electron travel, so that its momentum is equal to that of a photon of wavelength $663 \mathrm{~nm}$ ?
- $1098 \mathrm{~m} / \mathrm{s}$
- $109.8 \mathrm{~m} / \mathrm{s}$
- $10.98 \mathrm{~m} / \mathrm{s}$
- $1.098 \mathrm{~m} / \mathrm{s}$
Solution
$
\begin{aligned}
& \lambda=\frac{h}{m v} \\
& v=\frac{h}{m \lambda}
\end{aligned}
$
Given,
$
\begin{aligned}
\lambda & =663 \mathrm{~nm} \\
\lambda & =663 \times 10^{-9} \mathrm{~m} \\
h & =6.6 \times 10^{-34} \mathrm{Js} \\
m & =9.1 \times 10^{-31} \mathrm{~kg} \\
\nu & =\frac{6.6 \times 10^{-34}}{9.1 \times 10^{-31} \times 663 \times 10^{-9}} \\
& =0.0010979 \times 10^6 \simeq 1098 \mathrm{~m} / \mathrm{s} .
\end{aligned}
$
Asked in: AP EAMCET 2021 (23 Aug Shift 1)
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