Uncertainty in the position of an electron (mass $=9.1 \times 10^{-31} \mathrm{~kg}$ ) moving with a velocity $300 \mathrm{~ms}^{-1}$, accurate upto $0.001 \%$, will be ( $\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}$ )

(C) $1.92 \times 10^{-2} \mathrm{~m}$

(A) $19.2 \times 10^{-2} \mathrm{~m}$

(B) $5.76 \times 10^{-2} \mathrm{~m}$

(D) $3.84 \times 10^{-2} \mathrm{~m}$

JEE Main · 2006 · 30 Apr 2006 · Offline · Atomic Structure

Uncertainty in the position of an electron (mass

= 9.1 \times 1 0^{- 31} kg

) moving with a velocity

300 ms^{- 1}

, accurate upto

0.001%

, will be
(

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

)

Answer: (C)

Heisenberg's principle in the form

Δ x Δ v \geq \frac{h}{4 π m}

links the uncertainties in position and velocity. The velocity is known to

0.001%

300 m s^{- 1}

, so

Δ v = 300 \times \frac{0.001}{100} = 3 \times 1 0^{- 3} m s^{- 1}

. Substituting,

Δ x = \frac{6.63 \times 1 0 ^{- 34}}{4 \times 3.14 \times 9.1 \times 1 0 ^{- 31} \times 3 \times 1 0 ^{- 3}} \approx 1.92 \times 1 0^{- 2} m

, the minimum uncertainty in the electron's position.

JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option