Q141 / 150 · MHT CET 2023 (11 May Shift 1) · Physics

An electron moving with velocity $1.6 \times 10^7 \mathrm{~m} / \mathrm{s}$ has wavelength of $0.4 Å$. The required accelerating voltage for the electron motion is [charge on electron $=1.6 \times 10^{-19} \mathrm{C}$, mass of electron $\left.=9 \times 10^{-31} \mathrm{~kg}\right]$

  • A
    $7.2 \times 10^3 \mathrm{~V}$
  • Correct answer
    B
    $7.2 \times 10^2 \mathrm{~V}$
  • C
    $7.2 \mathrm{~V}$
  • D
    $7.2 \times 10^{-2} \mathrm{~V}$

Solution

When an electron is accelerated through a voltage its kinetic energy is converted into electric potential energy: $$ \begin{aligned} \mathrm{K} & =\mathrm{U} \\ & \frac{1}{2} \mathrm{mv}^2=\mathrm{eV} \\ \therefore \quad \mathrm{V} & =\frac{\mathrm{mv}^2}{2 \mathrm{e}} \\ & \mathrm{V}=\frac{\left(9 \times 10^{-31}\right)\left(1.6 \times 10^7\right)^2}{2 \times 1.6 \times 10^{-19}}=7.2 \times 10^2 \mathrm{~V} \end{aligned} $$

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

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