Question

Two electrons moving in opposite direction with speeds 0.8c and 0.4c where \( c \) is the speed of light in vacuum. Then the relative speed is about

• A. 0.4c
• B. 0.8c
• C. 0.9c
• D. 1.2c

Hint:

Use the relativistic velocity addition formula to calculate relative speeds when particles move in opposite directions at relativistic speeds.

Answer 1

The Correct Option is C

Step 1: Using relativistic velocity addition formula.
When two particles are moving in opposite directions, the relative speed \( v \) is given by the relativistic velocity addition formula: \[ v = \frac{v_1 + v_2}{1 + \frac{v_1 v_2}{c^2}} \] where \( v_1 = 0.8c \) and \( v_2 = 0.4c \).
Step 2: Substituting the values.
\[ v = \frac{0.8c + 0.4c}{1 + \frac{(0.8c)(0.4c)}{c^2}} = \frac{1.2c}{1 + 0.32} = \frac{1.2c}{1.32} \approx 0.9c \]
Step 3: Conclusion.
Hence, the correct answer is option (3).

Final Answer: \[ \boxed{0.9c} \]