If uncertainities in the measurement of position and momentum of a microscopic object of mass ' $m$ are…

If uncertainities in the measurement of position and momentum of a microscopic object of mass ' $m$ are equal, then the uncertainty in the measurement of velocity is given by the expression
  1. $\sqrt{\frac{h}{4 \pi m}}$
  2. $\sqrt{\frac{h}{4 \pi}} \times \frac{1}{m}$
  3. $\frac{h}{4 \pi} \times \sqrt{\frac{1}{m}}$
  4. $\sqrt{\frac{h}{2 \pi m}}$

Solution

According to Heisenberg's uncertainity principle. It is impossible to determine simultaneously the position and momentum of moving particle thus. $ \Delta x \times \Delta p \geq \frac{h}{4 \pi} $ But, $\quad p=m \times v$ $ \begin{array}{rlrl} & \therefore & \Delta v^2 & =\frac{h}{m^2 4 \pi} \\ \text { or } & \Delta v & =\sqrt{\frac{h}{4 \pi}} \times \frac{1}{m} \end{array} $

Asked in: AP EAMCET 2018 (23 Apr Shift 1)

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