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/(2 m).
In the light of the above statements, choose the correct answer from the options given below :

Solution

Chemistry ma’am · 4 steps

Statement I is the uncertainty principle itself; for II, set the two uncertainties equal and take a root.

1. Statement I. This is Heisenberg's uncertainty principle in words. Position and momentum cannot both be known exactly at the same time, so Statement I is true.

   Δ x · Δ p ≥ h/4π

2. Equal uncertainties. Put Δ x = Δ p, so (Δ p)² ≥ h/4π. Taking the square root, Δ p ≥ √(h/4π) = 1/2√(h/π).
3. Uncertainty in velocity. Since Δ p = m Δ v, divide by m: Δ v ≥ √(h/π) × 1/2m. This matches Statement II exactly, so it is true.
4. So. Both statements are true, which is option (b).

The idea to keep. When Δ x = Δ p, the product becomes (Δ p)². Take the root of h/4π, pull the 2 out of the root, then divide by m to reach Δ v.

Answer from the NTA final answer key. Solution by PrepWiser.