JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Atomic Structure

A ball weighing 10 g is moving with a velocity of

90 ms^{- 1}

. If the uncertainty in its velocity is

5%

, then the uncertainty in its position is ____

\times 1 0^{- 33} m

. (Rounded off to the nearest integer)
[Given:

h = 6.63 \times 1 0^{- 34} Js

]

Answer: 1

Solution

Heisenberg's uncertainty principle:

Δ x \cdot Δ p \geq \frac{h}{4 π}

. Here

Δ v = 0.05 \times 90 = 4.5

m/s,

m = 10

= 0.01

kg, so

Δ p = m Δ v = 0.01 \times 4.5 = 0.045

kg·m/s. Then

Δ x \geq \frac{6.63 \times 1 0 ^{- 34}}{4 \times 3.14 \times 0.045} \approx \frac{6.63 \times 1 0 ^{- 34}}{0.565} \approx 1.17 \times 1 0^{- 33}

\approx 1 \times 1 0^{- 33}

JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Integer answer