Question

The approximate mass of an electron is 10⁻²⁷ g. Calculate the uncertainty in its velocity if the uncertainty in its position were of the order of 10⁻¹¹m .

Answer 1

According to Heisenberg's uncertainty principle,
∆v = h/4πm∆x
Here ∆v is uncertainty in velocity
∆x is uncertainty in position.

Here, ∆x = 10⁻¹¹m , m = 10⁻²⁷ g = 10⁻³⁰ kg
h = 6.626 × 10⁻³⁴ J.s
Now, ∆v = 6.626 × 10⁻³⁴/(4 × 3.14 × 10⁻³⁰ × 10⁻¹¹)
= 6.626 × 10⁷/(12.56)
= 0.527 × 10⁷ m/s

Hence, uncertainty in velocity = 5.27 × 10⁶ m/s

Answer 2

Answer:

corect ans is 5.25×10^(6) m/s