Question

A green ball weighs $75\;g$ and comes travelling towards the observer at $400\;cm\;{\sec ^{ - 1}}$ A photon of light emitted from the green ball has a wavelength of $5 \times {10^{ - 5}}\;cm$ . Assuming that the error in the position of the ball is the same as the wavelength of itself, calculate the error in the momentum of the green ball.

Answer 1

Hint : The Heisenberg certainty principle states that the position and velocity of an object can -not be measured exactly at the same time. We have been given the mass of the ball and the wavelength associated with it. So we will calculate the error in the momentum of the green ball according to it.

Complete Step By Step Answer:
We have been given the weight of the green ball which is $75\;g$
Speed of the observer $=$ $400\;cm\;{\sec ^{ - 1}}$
Wavelength $= 5 \times {10^{ - 5}}\;cm$
Then according to the Heisenberg uncertainty principle,
$\Delta x.\Delta p = \dfrac{h}{{4\pi }}$
$\Delta p = \dfrac{h}{{4\pi \Delta x}}$
$\Rightarrow \Delta p = \dfrac{{6.626 \times {{10}^{ - 27}}}}{{4\pi \times 5 \times {{10}^{ - 5}}}}$
$\Rightarrow \Delta p = 1.055 \times {10^{ - 23}}$
Hence the error in the momentum of the green ball is $1.055 \times {10^{ - 23}}$

Note :
The Heisenberg uncertainty principle was given in keeping the view in mind the quantum mechanical model of atoms. It could not determine position and momentum at the same time. It was one of the important laws made for the study of the atom quantitatively.