Based on Heisenberg's uncertainty principle, the uncertainty in the velocity of the electron to be found within an atomic nucleus of diameter � m is ____

Heisenberg Uncertainty Principle Velocity of Electron | JEE Main PYQ | Structure of Atom

Q. Based on Heisenberg's uncertainty principle, the uncertainty in the velocity of the electron to be found within an atomic nucleus of diameter 10⁻¹⁵ m is _____ × 10⁹ m s⁻¹ (nearest integer).

Given : mass of electron = 9.1 × 10⁻³¹ kg
Planck's constant (h) = 6.626 × 10⁻³⁴ J s
Value of π = 3.14

Explanation

Step 1: Heisenberg Uncertainty Principle

Δx · Δp ≥ h / 4π

Step 2: Convert momentum uncertainty to velocity

Δp = m · Δv
Δv ≥ h / (4π m Δx)

Step 3: Substitute values

Δx = 10⁻¹⁵ m
m = 9.1 × 10⁻³¹ kg

Δv ≥ 6.626 × 10⁻³⁴ / (4 × 3.14 × 9.1 × 10⁻³¹ × 10⁻¹⁵)

Δv ≈ 5.8 × 10¹⁰ m s⁻¹

Correct Answer = 58

Previous Year Questions – Structure of Atom

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