What is de Broglie's wavelength for a particle having mass $6.64 \times 10^{-27} \mathrm{~kg}$ moving with…

What is de Broglie's wavelength for a particle having mass $6.64 \times 10^{-27} \mathrm{~kg}$ moving with velocity of $3 \times 10^3 \mathrm{~ms}^{-1} ?\left[\mathrm{~h}=6.63 \times 10^{-34} \mathrm{Js}\right]$
  1. 0.111 nm
  2. 0.0333 nm
  3. 1.22 nm
  4. 2.42 nm

Solution

$\begin{aligned} & \lambda=\frac{\mathrm{h}}{\mathrm{mv}}=\frac{6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}}{6.64 \times 10^{-27} \mathrm{~kg} \times 3 \times 10^3 \mathrm{~ms}^{-1}} \\ & =0.0333 \times 10^{-9} \mathrm{~m} \\ & =0.033 \mathrm{~nm}\end{aligned}$

Asked in: MHT CET 2024 (16 May Shift 2)

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