Suppose you have an electron and an alpha particle ( nucleus of a helium atom) t

Question

Suppose you have an electron and an alpha particle ( nucleus of a helium atom) through a piece of beam pipe inside a particle accelerator. The particles are traveling in the same direction. The speed of the electron is 0.830c and the speed of the alpha particle is 0.750c, both measured by a stationary observer in the lab. What is the speed of the alpha particle as observed from the electron, in units of the speed of light. Suppose you have an electron and an alpha particle ( nucleus of a helium atom) through a piece of beam pipe inside a particle accelerator. The particles are traveling in the same direction. The speed of the electron is 0.830c and the speed of the alpha particle is 0.750c, both measured by a stationary observer in the lab. What is the speed of the alpha particle as observed from the electron, in units of the speed of light.

Explanation / Answer

Speed of electron = u = 0.83 c

Speed of alpha = v = 0.75 c

speed of the alpha particle as observed from the electron = w = ( u + v ) / ( 1 + uv/c^2 )

= ( 0.83 c + 0.75 c ) / ( 1 + (0.83 c x 0.75 c) /c^2 )

= (0.83 + 0.75) c / ( 1 + 0.83*0.75 ) = 0.974 c

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