The de Broglie wavelength of an electron travelling with $20 \%$ of velocity of light is $\left(\mathrm{h}=6…

The de Broglie wavelength of an electron travelling with $20 \%$ of velocity of light is $\left(\mathrm{h}=6.626 \times 10^{-34} \mathrm{JS} ; \mathrm{m}_{\mathrm{e}}=9.1 \times 10^{-31} \mathrm{~kg}\right)$
  1. $2.4 \times 10^{-11} \mathrm{~m}$
  2. $1.2 \times 10^{-11} \mathrm{~m}$
  3. $3.6 \times 10^{-11} \mathrm{~m}$
  4. $4.8 \times 10^{-11} \mathrm{~m}$

Solution

$\mathrm{C}=3 \times 10^8 \mathrm{~ms}^{-1}$ $\Rightarrow \operatorname{Velocity}(V)=\frac{20 \times 3 \times 10^8}{100}=6 \times 10^7 \mathrm{~ms}^{-1}$ Thus, $\lambda=\frac{\mathrm{h}}{\mathrm{m}_{\mathrm{e}} \mathrm{V}}=\frac{6.626 \times 10^{-34}}{\left(9.1 \times 10^{-31}\right)\left(6 \times 10^7\right)}$ $=1.2 \times 10^{-11} \mathrm{~m}$.

Asked in: AP EAMCET 2023 (15 May Shift 2)

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