Q17 / 75 · JEE Main 2025 (29 Jan Shift 2) · Chemistry

Given below are two statements : Statement (I) : It is impossible to specify simultaneously with arbitrary precision, both the linear momentum and the position of a particle. Statement (II) : If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron, then the uncertainty in the measurement of velocity is $\geqslant \sqrt{\frac{\mathrm{h}}{\pi}} \times \frac{1}{2 \mathrm{~m}}$. In the light of the above statements, choose the correct answer from the options given below :

  • A
    Statement I is false but Statement II is true
  • B
    Both Statement I and Statement II are false
  • Correct answer
    C
    Both Statement I and Statement II are true
  • D
    Statement I is true but Statement II is false

Solution

According to Heisenberg's uncertainty principle, it is impossible to determine simultaneously the exact position and momentum of particle like electron If $\begin{aligned} & \Delta p=\Delta x \\ & \Delta p \cdot \Delta x \geq \frac{h}{4 \pi} \\ &(\Delta p)^2 \geq \frac{h}{4 \pi} \\ & \Delta p \geq \sqrt{\frac{h}{\pi}} \times \frac{1}{2} \\ & m \Delta v \geq \sqrt{\frac{h}{\pi}} \times \frac{1}{2} \\ & \Delta v \geq \sqrt{\frac{h}{\pi}} \times \frac{1}{2 m}\end{aligned}$

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

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