A bullet of mass 5.0 g moves at 400 m s^-1, with the speed known to within 0.0010 %. Using Delta x Delta p = h/4pi with h = 6.626x10^-34 J s, find the minimum uncertainty in position in units of 10^-30 m, to two decimals.

JEE Advanced levelNumerical answerDifficulty 3 of 3as151

A bullet of mass $5.0 g$ moves at $400 m s^{- 1}$ , with the speed known to within $0.0010 %$ . Using $Δ x Δ p = h /4 π$ with $h = 6.626 \times 1 0^{- 34} J s$ , find the minimum uncertainty in position in units of $1 0^{- 30} m$ , to two decimals.

Numerical answer type, answer in 1e-30 m, tolerance 0.02.

Δ v = 400 \times 1 0^{- 5} = 4.0 \times 1 0^{- 3} m s^{- 1}

Δ p = 5.0 \times 1 0^{- 3} \times 4.0 \times 1 0^{- 3} = 2.0 \times 1 0^{- 5} kg m s^{- 1}

Δ x = h / (4 π Δ p) = 2.636 \times 1 0^{- 30} m