Question

g) Two electrons are ejected in opposite directions from a radioactive material at rest in the laboratory. Each electron has a speed of 0.8c as measured by a laboratory observer. What is the speed of one electron as measured by the other? Write 4-momentum equations and comment about invariant property of 4-momentum.

Answer 1

1) Relative Velocity is defined as , $\vec{V_{12}}=\vec{V_{1}}-\vec{V_{2}}$

Where V12 represents Velocity of 1 with respect to 2

therefore,

$\vec{V_{12}}=0.8c-(-0.8c)=1.6c$

and direction will be in the same as that for the individual one depends on which one relative to whom we are calculating the "Relative Velocity".

2) Momentum is invariant in nature despite of having the force is Conservative or Non-Conservative, it will always remains conserved/constant. Since in this case body was in rest so that's why we have the velocity of two electron same but in different direction after emission so initial momentum will be equal to final momentum.

Conservation of momentum,

initial momentum= final momentum

$0=(m_{e}\times 0.8c)+(m_{e}\times (-0.8c))$

$=0$

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