Question

In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%. Certainty with which the position of the electron can be located is ______.

(h = 6.6 × 10⁻³⁴ kg m²s⁻¹, mass of electron, e_m = 9.1 × 10⁻³¹ kg)

Options

• 5.10 × 10⁻³ m

• 1.92 × 10⁻³ m

• 3.84 × 10⁻³ m

• 1.52 × 10⁻⁴ m

Answer 1

1.92 × 10⁻³ m

Explanation:

According to the Heisenberg uncertainty principle,

Δx.mΔv = `"h"/(4π)`; Δx = `"h"/(4π"m"Δ"v")`

Here Δv = `(600 xx 0.005)/100` = 0.03 m/s

So, Δx = `(6.6 xx 10^-34)/(4 xx 3.14 xx 9.1 xx 10^-31 xx 0.03)`

= 1.92 × 10⁻³ m