Q24 / 125 · BITSAT 2021 · Chemistry

Calculate the wavelength (in nanometer) associated with a proton moving at $1.0 \times 10^{3} \mathrm{~ms}^{-1}$. (Mass of proton $=1.67 \times 10^{-27} \mathrm{~kg}$ and $\left.\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}\right)$

  • Correct answer
    A
    $0.40 \mathrm{~nm}$
  • B
    $2.5 \mathrm{~nm}$
  • C
    $14.0 \mathrm{~nm}$
  • D
    $0.32 \mathrm{~nm}$

Solution

$\begin{aligned} \lambda &=\frac{h}{m v}=\frac{6.63 \times 10^{-34}}{1.67 \times 10^{-27} \times 1 \times 10^{3}} \\ &=3.97 \times 10^{-10} \text { meter }=0.397 \text { nanometer } \approx 0.40 \mathrm{~nm} \end{aligned}$

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

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