Question

A β particle (a free electron) is speeding around the track in a cyclotron, rapidly gaining speed. How will the particle’s momentum change as its speed approaches the speed of light? Explain.

a) Momentum increases linearly.

b) Momentum increases exponentially.

c) Momentum approaches infinity.

d) Momentum approaches a constant value.

Answer 1

As a β particle (a free electron) speeds up in a cyclotron and approaches the speed of light, its momentum will approach a constant value, according to Einstein's theory of relativity.

Step-by-step explanation:

As a β particle (a free electron) speeds up in a cyclotron and approaches the speed of light, its momentum will approach a constant value. This means that its momentum will not increase exponentially or approach infinity. The reason for this is that as an object with mass approaches the speed of light, its momentum increases at a decreasing rate. This behavior is described by Einstein's theory of relativity, which states that the momentum of an object with mass increases towards infinity as it approaches the speed of light, but its speed approaches a constant value.