An electron has a speed of 50 m / s with uncertainty of 0.02 %. The uncertainty in locating its position is

Question

An electron has a speed of 50 m / s with uncertainty of 0.02 %. The uncertainty in locating its position is (A) 1.1 × 10-1 m (B) 3.2 × 10-7 m (C) 1.2 × 10-5 m (D) 5.8 × 10-3 m

Tardigrade Admin · Accepted Answer

Δ v =(0.02/100) × 50=0.01 According of Heisenberg's uncertainty principle, Δ x × Δ v =( h /4 π m ) Δ x =(6.6 × 10-34/4 × 3.14 × 9.1 × 10-31 × 0.01) =5.77 × 10-3 m ≈ 5.8 × 10-3 m

Q. An electron has a speed of $50 m / s$ with uncertainty of $0.02%$ . The uncertainty in locating its position is

$1.1 \times 1 0^{- 1} m$

$3.2 \times 1 0^{- 7} m$

$1.2 \times 1 0^{- 5} m$

$5.8 \times 1 0^{- 3} m$

$Δ v = \frac{0.02}{100} \times 50 = 0.01$
According of Heisenberg's uncertainty principle,
$Δ x \times Δ v = \frac{h}{4 πm}$
$Δ x = \frac{6.6 \times 1 0 ^{- 34}}{4 \times 3.14 \times 9.1 \times 1 0 ^{- 31} \times 0.01}$
$= 5.77 \times 1 0^{- 3} m$
$\approx 5.8 \times 1 0^{- 3} m$

Q. An electron has a speed of 50m/s with uncertainty of 0.02%. The uncertainty in locating its position is

1.1×10−1m

3.2×10−7m

1.2×10−5m

5.8×10−3m