Question

Using uncertainity principle, calculate the uncertainty in velocity of an electron if the uncertainty in position is 10⁻⁴ m.

Answer 1

Use Uncertainty principle ,
e.g., ∆x.m∆v = h/4π
Here, ∆x is uncertainty in position
∆v is uncertainty in velocity
m is mass of particle

Here, ∆x = 10⁻⁴ m , m = 9.1 × 10⁻³¹ kg and h = 6.626 × 10⁻³⁴ J.s
Now, ∆v = h/4πm∆x
= 6.626 × 10⁻³⁴/{ 4 × 3.14 × 9.1 × 10⁻³¹ × 10⁻⁴}
= 66.26/(4 × 3.14 × 9.1 )
= 0.579 m/s

Hence, uncertainty in velocity = 0.579 m/s