A radioactive atom is traveling through the laboratory at a speed of 0.2c when it undergoes beta decay.The emitted electron moves in the same direction as the atom and has a speed of 0.9c relative to the atom.The speed of the electron,as seen by an observer in the laboratory,is
A)1.10c
B)1.07c
C)c
D)0.93c
E)0.70c

Question

Quizplus · Accepted Answer

We will use the relativistic velocity addition formula to find the speed of the electron as seen by the observer in the laboratory:

v_lab = (v_atom + v_e) / (1+ v_atom*v_e/c^2)

Where v_atom = 0.2c (given), v_e = 0.9c (given) and c is the speed of light.

v_lab = (0.2c + 0.9c) / (1 + (0.2c)*(0.9c)/c^2)

v_lab = 1.1c / (1 + 0.18)

v_lab = 1.1c / 1.18

v_lab = 0.932c

So the speed of the electron as seen by an observer in the laboratory is 0.932c, which is closest to choice D: 0.93c.

A Radioactive Atom Is Traveling Through the Laboratory at a Speed