Question

The minimum uncertainty in the speed of an electron in an one dimensional region of length 2a₀ (Where a₀ = Bohr radius 52.9 pm) is _____ km s^–1.
(Given : Mass of electron = 9.1 × 10^–31 kg, Planck’s constant h = 6.63 × 10^–34Js)

Answer 1

Correct Answer: 548

According to the uncertainty principle,
\(\Delta x \cdot \Delta v \geq \frac{\hbar}{4\pi m}\)

\(\Delta x = 2 \times 52.9 \times 10^{-12} \, \text{m}\)

\(\Delta v \geq \frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 10^{-31} \times 2 \times 52.9 \times 10^{-12}} \)

\(\Delta v \geq 5.48 \times 10^{-4} \times 10^9 \, \text{m/s}\)
\(Δv≥548 km/s\)
So, the correct answer is 548.