Question

The muzzle velocity of a rifle bullet is 709 m s−1along the direction of motion. If the bullet weighs 35 g, and the uncertainty in its momentum is 0.20%, how accurately can the position of the bullet be measured along the direction of motion?

Answer 1

Answer:

Uncertainty in position of the bullet is $\Delta x=1.07\times 10^{-33}\ m$

Explanation:

It is given that,

Mass of the bullet, m = 35 g = 0.035 kg

Velocity of bullet, v = 709 m/s

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

$p=mv$

$p=0.035\times 709=24.81\ kg-m/s$

Uncertainty in momentum is,

$\Delta p=0.2\%\ of\ 24.81$

$\Delta p=0.049$

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

$\Delta p.\Delta x\geq \dfrac{h}{4\pi}$

$\Delta x=\dfrac{h}{4\pi \Delta p}$

$\Delta x=\dfrac{6.62\times 10^{-34}}{4\pi \times 0.049}$

$\Delta x=1.07\times 10^{-33}\ m$

Hence, this is the required solution.