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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 ≥ [h/π] × 1/2m. In the light of the above statements, choose the correct answer from the options given below :

1. Statement I is true but Statement II is false.
2. Both Statement I and Statement II are true.
3. Statement I is false but Statement II is true.
4. Both Statement I and Statement II are false.

Correct answer: Both Statement I and Statement II are true.

Solution

Statement I is true as it reflects the Heisenberg Uncertainty Principle, which states that position and momentum cannot both be precisely known at the same time. Statement II is also true because it correctly derives the relationship between uncertainties in position and momentum, leading to a minimum uncertainty in velocity.

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