Free ²³⁸U nuclei kept in a train emit alpha particles. When the train is stationary and a uranium nucleus decays, a passenger measures that the separation between the alpha particle and the recoiling nucleus becomes x in time t after the decay. If a decay takes place when the train is moving at a uniform speed v, the distance between the alpha particle and the recoiling nucleus at a time t after the decay, as measured by the passenger will be
(a) x + vt
(b) x − vt
(c) x
(d) depends on the direction of the train.

Open in App

Solution

(c) x

When the train is stationary, the separation between the alpha particle and recoiling uranium nucleus is x in time t after the decay. Even if the decay is taking place in a moving train and the separation is measured by the passenger sitting in it, the separation between the alpha particle and nucleus will be x. This is because the observer is also moving with the same speed with which the alpha particle and recoiling nucleus are moving, i.e. they all are in the same frame that is moving at a uniform speed.

Suggest Corrections

Similar questions

Q. A free

{}^{238}U

nucleus kept in a train emits an alpha particle. When the train is stationary, a nucleus decays and a passenger measures that the separation between the alpha particle and the recoiling nucleus becomes x at time t after the decay. If the decay takes place while the train is moving at a uniform velocity v, the distance between the alpha particle and the recoiling nucleus at a time t after the decay, as measured by the passenger, is
(a) x + v t
(b) x − v t
(c) x
(d) depends on the direction of the train

Q. Free

^{238} U

nuclei kept in a train emit alpha particles. When the train is stationary and a uranium nucleus decays, a passenger measures that the separation between the alpha particles and the recoiling nucleus becomes

x

, in

t

time after the decay. If a decay takes places, when the train is moving at a uniform speed

v

, the distance between the alpha particle and the recoiling nucleus at a time

t

after the decay, as measured by the passenger will be

Q. A free

^{238}

U nucleus kept in a train emits an alpha particle. When the train is stationary, a nucleus decays and a passenger measures that the separation between the alpha particle and the recoiling nucleus becomes x at time t after the decay. If the decay takes place while the train is moving at a uniform velocity v, the distance between the alpha particle and the recoiling nucleus at a time t after the decay as measured by the passenger is:

A $^{238} U$ nucleus decays by emitting an alpha particle of speed $^{'} v^{'} m s^{- 1}$ . The recoil speed of the residual nucleus (in $m s^{- 1}$ ) is:

Q. When

U^{238}

nucleus originally at rest, decays by emitting an alpha particle having a speed

u

, the recoil speed of the residual nucleus is

Join BYJU'S Learning Program