If a 1.00 g body is travelling along the X -axis at 100 cm s -1 within 1 cm s -1, then uncertainity in its position is

Question

If a 1.00 g body is travelling along the X -axis at 100 cm s -1 within 1 cm s -1, then uncertainity in its position is (A) 1.318 × 10-30 m (B) 5.272 × 10-30 m (C) 2.636 × 10-30 m (D) 6.590 × 10-31 m

Tardigrade Admin · Accepted Answer

there is uncertainty with 1 cm s -1, hence, velocity varies between 99 cm s -1 to 101 cm s -1 Thus, Δ v (uncertainty in velocity) =101-99=2 cm s -1 =0.02 m s -1 By Heisenberg's uncertainty principle Δ x ⋅ Δ p ≈ (h/4 π) Δ x ⋅ m Δ v ≈ (h/4 π) ∴ Uncertainty in position, Δ x ≈ (h/4 π m Δ v) Δ x=(6.62 × 10-34 Js ( kg m 2 s -2)/4 π 1.0010-3 kg × 0.02 ms -1) =2.63 × 10-30 m

Q. If a $1.00 g$ body is travelling along the $X$ -axis at $100 c m$ $s^{- 1}$ within $1 c m s^{- 1}$ , then uncertainity in its position is

$1.318 \times 1 0^{- 30} m$

$5.272 \times 1 0^{- 30} m$

$2.636 \times 1 0^{- 30} m$

$6.590 \times 1 0^{- 31} m$

Q. If a 1.00g body is travelling along the X -axis at 100cm s−1 within 1cms−1, then uncertainity in its position is

1.318×10−30m

5.272×10−30m

2.636×10−30m

6.590×10−31m

Q. If a $1.00 g$ body is travelling along the $X$ -axis at $100 c m$ $s^{- 1}$ within $1 c m s^{- 1}$ , then uncertainity in its position is

$1.318 \times 1 0^{- 30} m$

$5.272 \times 1 0^{- 30} m$

$2.636 \times 1 0^{- 30} m$

$6.590 \times 1 0^{- 31} m$