Calculate the minimum uncertainty in velocity of a particle of mass 1.1 × 10-27 kg if uncertainty in its position is 3 × 10-10 cm.

Question

Calculate the minimum uncertainty in velocity of a particle of mass 1.1 × 10-27 kg if uncertainty in its position is 3 × 10-10 cm. (A) 1.5 × 10-4 m (B) 2.5× 10-4 m (C) 3.5 × 10-4 m (D) 4.5 × 10-4 m

Tardigrade Admin · Accepted Answer

Δ x. Δ ge (h/4π m) Δ v ge(h/Δ x.4π.m) =(6.6×10-34/3×10-10×10-2m×4×3.14×1.1×10-27) =1.5×10-4 m

Q. Calculate the minimum uncertainty in velocity of a particle of mass $1.1 \times 1 0^{- 27}$ kg if uncertainty in its position is $3 \times 1 0^{- 10}$ cm.

$1.5 \times 1 0^{- 4}$ m

$2.5 \times 1 0^{- 4} m$

$3.5 \times 1 0^{- 4} m$

$4.5 \times 1 0^{- 4} m$

$Δ x .Δ \geq \frac{h}{4 πm}$
$Δ v \geq \frac{h}{Δ x .4 π . m}$
$= \frac{6.6 \times 1 0 ^{- 34}}{3 \times 1 0 ^{- 10} \times 1 0 ^{- 2} m \times 4 \times 3.14 \times 1.1 \times 1 0 ^{- 27}}$
$= 1.5 \times 1 0^{- 4} m$

Q. Calculate the minimum uncertainty in velocity of a particle of mass 1.1×10−27 kg if uncertainty in its position is 3×10−10 cm.

1.5×10−4 m

2.5×10−4m

3.5×10−4m

4.5×10−4m