To find the uncertainty in velocity (Δ v), we apply Heisenberg's Uncertainty Principle:
Δ x ⋅ Δ p ≥ 4πh
Since Δ p = m Δ v, we rearrange the formula to solve for velocity:
Δ v = 4π ⋅ m ⋅ Δ xh
Using the provided constants:
h: 6.626 × 10−34 J s
m: 9.1 × 10−31 kg
Δ x: 10−15 m
π: 3.14
Δ v = 4 × 3.14 × 9.1 × 10−31 × 10−156.626 × 10−34
Δ v = 1.143 × 10−446.626 × 10−34
Δ v ≈ 5.797 × 1010 m s−1
To express this in terms of 109 m s−1:
Δ v ≈ 57.97 × 109 m s−1
Rounding to the nearest integer, the value is 58.