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:

This is a direct statement of Heisenberg Uncertainty Principle:
Δx · Δp ≥ h / 4π
Hence, position and momentum cannot be measured simultaneously with arbitrary precision.
✔ Statement I is true.

Given: Δx = Δp

Using uncertainty relation:
Δx · Δp ≥ h / 4π
(Δp)² ≥ h / 4π
Δp ≥ √( h / 4π )

Since momentum p = mv,
Δp = m Δv
⇒ Δv ≥ √( h / 4π ) / m

Which can be written as:
Δv ≥ √( h / π ) × 1 / (2m)
✔ Statement II is true.

Correct Answer = Both Statement I and Statement II are true