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JEE Main 202529 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
29 January
Shift
Evening Shift
Subject
Chemistry
Chapter
Structure of Atom

JEE Main 2025 · 29 January · Evening Shift · Chemistry · Structure of Atom

Given below are two statements : Statement (I) : It is impossible...

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 ⩾hπ×12 m\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 :

Options

  1. AStatement I is false but Statement II is true
  2. BBoth Statement I and Statement II are false
  3. CBoth Statement I and Statement II are true
  4. DStatement I is true but Statement II is false

Correct answer

C. Both Statement I and Statement II are true

Step-by-step solution

According to Heisenberg's uncertainty principle, it is impossible to determine simultaneously the exact position and momentum of particle like electron If Δp=ΔxΔp⋅Δx≥h4π(Δp)2≥h4πΔp≥hπ×12mΔv≥hπ×12Δv≥hπ×12m\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}
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