Q1 / 160 · AP EAMCET 2024 (20 May Shift 2) · Chemistry

If uncertainty in position and momentum of an electron are equal, then uncertainty in its velocity is

  • Correct answer
    A
    $\frac{1}{2 m} \sqrt{\frac{h}{\pi}}$
  • B
    $\frac{1}{m} \sqrt{\frac{h}{\pi}}$
  • C
    $\sqrt{\frac{h}{\pi}}$
  • D
    $m \sqrt{\frac{h}{\pi}}$

Solution

$\begin{aligned} & \Delta \mathrm{x} \times \Delta \mathrm{p}=\frac{\mathrm{h}}{4 \pi} \\ & \text { Given, } \Delta \mathrm{x} \times \Delta \mathrm{p} \\ & (\Delta \mathrm{p})^2=\frac{\mathrm{h}}{4 \pi} \Rightarrow \Delta \mathrm{p}=\sqrt{\frac{\mathrm{h}}{4 \pi}} \\ & \Rightarrow \mathrm{~m} \Delta \mathrm{v}=\frac{1}{2} \sqrt{\frac{\mathrm{~h}}{\pi}} \\ & \Rightarrow \Delta \mathrm{v}=\frac{1}{2 \mathrm{~m}} \sqrt{\frac{\mathrm{~m}}{\pi}}\end{aligned}$

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

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