The uncertainty in position and velocity of a particle are 10-10 m and 5.27 × 10-24 ms-1 respectively. Calculate the mass of the particle is (h = 6.625 × 10-34 J-s)

Question

The uncertainty in position and velocity of a particle are 10-10 m and 5.27 × 10-24 ms-1 respectively. Calculate the mass of the particle is (h = 6.625 × 10-34 J-s)  (A) 0.099 kg (B) 0.99 kg (C) 0.92 kg (D) None

Tardigrade Admin · Accepted Answer

According to Heisenbergâs uncertainty principle, Δ x. m Δ v=(h/4π) or m=(h/4π Δ x. Δ v) =(6.625×10-34 Js/4×3.143×10-10 m×5.27×10-24 ms-1) ∵[J=Kgm2s2] =0.099 kg.

Q. The uncertainty in position and velocity of a particle are $1 0^{- 10} m$ and $5.27 \times 1 0^{- 24} m s^{- 1}$ respectively. Calculate the mass of the particle is $(h = 6.625 \times 1 0^{- 34} J - s)$

$0.099 k g$

$0.99 k g$

$0.92 k g$

None

According to Heisenberg’s uncertainty principle,
$Δ x . m Δ v = \frac{h}{4 π}$
or $m = \frac{h}{4 π Δ x . Δ v}$
$= \frac{6.625 \times 1 0 ^{- 34} J s}{4 \times 3.143 \times 1 0 ^{- 10} m \times 5.27 \times 1 0 ^{- 24} m s ^{- 1}}$
$∵ [J = K g m^{2} s^{2}]$
$= 0.099 k g .$

Q. The uncertainty in position and velocity of a particle are 10−10m and 5.27×10−24ms−1 respectively. Calculate the mass of the particle is (h=6.625×10−34J−s)

0.099kg

0.99kg

0.92kg