How much energy is imparted to an electron so that its de-Broglie wavelength reduces from $10^{-10}…

How much energy is imparted to an electron so that its de-Broglie wavelength reduces from $10^{-10} \mathrm{~m}$ to $0 \cdot 5 \times 10^{-10} \mathrm{~m} ?(\mathrm{E}=$ energy of electron $)$
  1. $4 \mathrm{E}$
  2. $2 \mathrm{E}$
  3. $3 \mathrm{E}$
  4. $\mathrm{E}$

Solution

$\lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}$ $\frac{\lambda_{1}}{\lambda_{2}}=\sqrt{\frac{\mathrm{E}_{2}}{\mathrm{E}_{1}}} \Rightarrow \frac{1 \times 10^{-10}}{0.5 \times 10^{-10}}=\sqrt{\frac{\mathrm{E}_{2}}{\mathrm{E}_{1}}}$ $\therefore 2=\sqrt{\frac{\mathrm{E}_{2}}{\mathrm{E}_{1}}} \quad \therefore \frac{\mathrm{E}_{2}}{\mathrm{E}_{1}}=4$ $\therefore \mathrm{E}_{2}=4 \mathrm{E}_{1}$

Asked in: MHT CET 2020 (15 Oct Shift 1)

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