Question

A cricket ball weighs 200g . If the uncertainty in itself position is 5pm .What is the uncertainty in the velocity of the ball?

Answer 1

Answer :-

$\Delta V = 5.04 \times 10^{-21} m/s$

Given :-

Mass of ball = 200 g or 0.2 kg

Uncertainty in its position = 5 pm

To find :-

Uncertainty in the velocity of ball.

Solution:-

Let the uncertainty in the velocity be $\Delta {V}$

According to hesisenberg principal of uncertainty.

→$\Delta X \times \Delta P \geqslant \dfrac{h}{4\pi}$

→$\Delta X \times \Delta V = \dfrac{h}{4 \pi m }$

• Put the given values.

→$5 \times 10^{-12} \times \Delta V = \dfrac{6.34 \times10^{-34} }{4 \times 3.14 \times 0.2}$

→$5 \times 10^{-12} \times \Delta V = \dfrac{6.34\times 10^{-34}}{2.512}$

→$\Delta V = \dfrac{6.34\times 10^{-34}}{2.512 \times5 \times 10^{-12} }$

→$\Delta V = \dfrac{6.34\times 10^{-34}}{12.56 \times 10^{-12}}$

→$\Delta V = 5.04 \times 10^{-21} m/s$

hence,

The uncertainty in the velocity of the ball is $5.04 \times 10^{-21} m/s .$