What will be the uncertainty in velocity of an electron when the uncertainty in its position is 1000 mathringA ?

Question

What will be the uncertainty in velocity of an electron when the uncertainty in its position is 1000 mathringA ? (A) 5.79 × 102 m s-1 (B) 5.79 × 108 m s-1 (C) 5.79 × 104 m s-1 (D) 5.79 × 10-10 m s-1

Tardigrade Admin · Accepted Answer

Δ x ⋅ mΔ v=(h/4π) Δ x=100 mathringA =1000×10-10 m or 10-7 m Δ v=(6.626 × 10-34 J s/4 ×3.14 ×9.1 × 10-31 kg × 10-7 m) =5.79×102 m/s

Q. What will be the uncertainty in velocity of an electron when the uncertainty in its position is $1000 \overset{˚}{A}$ ?

$5.79 \times 1 0^{2} m s^{- 1}$

$5.79 \times 1 0^{8} m s^{- 1}$

$5.79 \times 1 0^{4} m s^{- 1}$

$5.79 \times 1 0^{- 10} m s^{- 1}$

$Δ x \cdot m Δ v = \frac{h}{4 π}$
$Δ x = 100 \overset{˚}{A} = 1000 \times 1 0^{- 10} m$ or $1 0^{- 7} m$
$Δ v = \frac{6.626 \times 1 0 ^{- 34} J s}{4 \times 3.14 \times 9.1 \times 1 0 ^{- 31} k g \times 1 0 ^{- 7} m}$
$= 5.79 \times 1 0^{2} m / s$

Q. What will be the uncertainty in velocity of an electron when the uncertainty in its position is 1000A˚?

5.79×102ms−1

5.79×108ms−1

5.79×104ms−1

5.79×10−10ms−1