If the uncertainty in velocity and position of a minute particle in space are, $2.4 \times 10^{-26}(\mathrm{~ms}^{-1})$ and $10^{-7}(\mathrm{~m})$ respectively. The mass of the particle in g is ______ (Nearest integer) (Given : $\mathrm{h}=6.626 \times 10^{-34} \mathrm{Js}$)

JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Atomic Structure

If the uncertainty in velocity and position of a minute particle in space are,

2.4 \times 1 0^{- 26} (ms^{- 1})

and

1 0^{- 7} (m)

respectively. The mass of the particle in g is ______ (Nearest integer)
(Given :

h = 6.626 \times 1 0^{- 34} Js

)

Answer: 22

Using Heisenberg's uncertainty principle:

Δ p \cdot Δ x \geq \frac{h}{4 π}

. Since

Δ p = m Δ v

, we have

m Δ v \cdot Δ x = \frac{h}{4 π}

. Substituting values:

m \times 2.4 \times 1 0^{- 26} \times 1 0^{- 7} = \frac{6.626 \times 1 0 ^{- 34}}{4 π}

. Solving:

m = \frac{6.626 \times 1 0 ^{- 34}}{2.4 \times 1 0 ^{- 33} \times 4 π} = \frac{6.626}{9.6 π} \times 1 0^{- 1}

= 0.02198

= 21.98

\approx 22

JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Integer answer