Question

At what speed would the mass of an electron become double of it's rest mass

Answer 1

Explanation:

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If the mass of the electron becomes double of its rest mass, then we can write:

mm0=2

Since m=m0γ , this means that:

γ=2

But γ is defined as:

γ=11−v2c2√

Thus,

11−v2c2√=2

11−v2c2=4

vc=34−−√

Therfore, the speed at which the mass of the electron becomes double of its mass:

mm0=2

Since m=m0γ, this means that:

γ=2

But γ is defined as:

γ=11−v2c2√

Thus,

11−v2c2√=2

11−v2c2=4

vc=34−−√

Therfore, the speed at which the mass of the electron becomes double of its mass:

v=34−−√c≈ 0.87⋅c

Meaning around 87% of the speed of light.

Notice that it does not even matter if we talk about the mass of the electron or any other particle. This holds for every massive particle (m0≠0). This is true in general; the speed at which the mass of a particle gets doubled with respect to its rest mass is around 87% of the speed of light. But the higher the rest mass of the particle, the harder it is to make it reach that speed.

Hope it helps you

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