Question

The muzzle velocity of a rifle bullet is 800. m⋅ s −1 m⋅s−1 along the direction of motion. If the bullet weighs 27.0 g g , and the uncertainty in its momentum is 0.200 % % , how accurately can the position of the bullet be measured along the direction of motion?

Answer 1

Answer:

1.98 × 10⁻³³m

Explanation:

It is given that,

Mass of the bullet, m = 27 g = 0.027 kg

Velocity of bullet, v = 800 m/s

The uncertainty in momentum is 0.20%. The momentum of the bullet is given by :

$p=mvp=0.027\times 800 = 21.6\ kg-m/s$

Uncertainty in momentum is,

$\Delta p=0.2\%\ of\ 21.6\\\Delta p=0.0432$

We need to find the uncertainty in position. It can be calculated using Heisenberg uncertainty principal as :

$\Delta p.\Delta x\geq \dfrac{h}{4\pi}\Delta x=\dfrac{h}{4\pi \Delta p}\Delta x=\dfrac{6.62\times 10^{-34}}{4\pi \times 0.0432}\Delta x=1.98\times 10^{-33}\ m$