JEE Main 2025 Jan 29 Shift 2, Chemistry Q15: Dual Character Of Matter And Radiation

JEE Main2025Jan 29, Shift 2Chemistry

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 $\geq \frac{h}{π} \times \frac{1}{2 m}$ .

In the light of the above statements, choose the correct answer from the options given below :

A
Statement I is true but Statement II is false.
B
Both Statement I and Statement II are true.
C
Statement I is false but Statement II is true.
D
Both Statement I and Statement II are false.

Solution

Statement I is a direct verbal form of Heisenberg’s uncertainty principle, $Δ x \cdot Δ p \geq \frac{h}{4 π}$ . True.

Statement II: Set $Δ x = Δ p = a$ . Then $a^{2} \geq \frac{h}{4 π}$ , so $a \geq \frac{h}{4 π}$ .

Since $Δ p = m Δ v$ , the velocity uncertainty satisfies

$Δ v = \frac{a}{m} \geq \frac{1}{m} \frac{h}{4 π} = \frac{1}{2 m} \frac{h}{π}$ .

This matches the given expression. True.

$∴$ Both statements are correct.

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JEE Main 2025 Jan 29 Shift 2, Chemistry Q15: Dual Character Of Matter And Radiation

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