Statement I: It is impossible to specify simultaneously with arbitrary precision, both the linear momentum and the position of a particle. [2025]

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Solution

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

In the light of the above statements, choose the correct answer from the options given below: [2025]

1 Both Statement I and Statement II are true

2 Statement I is false but Statement II is true

3 Statement I is true but Statement II is false

4 Both Statement I and Statement II are false

Ans.
(1)

Statement I: This is Heisenberg's Uncertainty Principle.

Statement II: $Δ x Δ p \geq \frac{h}{4 π}, Δ p Δ p \geq \frac{h}{4 π},$

$Δ p \geq \sqrt{\frac{h}{4 π}}, Δ v \geq \frac{1}{m} \sqrt{\frac{h}{4 π}}$

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