A free ²³⁸ U nucleus kept inside a train emits an alpha particle. When the train is stationary, a nucleus decays, and a passenger measures the separation between the alpha particle and the recoiling nucleus to be x at a time t after the decay. If the decay occurs 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 measur

Step-by-step solution

The separation between the alpha particle and the recoiling nucleus depends only on their relative velocity. Let the velocity of the alpha particle be v _ and that of the recoiling nucleus be v _ N in the frame of the train. The relative velocity is v _ rel = v _ - v _ N . Since the train moves with a uniform velocity v , it represents an inertial frame of reference. According to the principle of relativity, the laws of physics are identical in all inertial frames. The energy released in the decay and the conservat