Question regarding the mass of an alpha particle when travelling at a speed approaching the speed of light [duplicate]

The speed of an Alpha particle is: 10^7 m/s.

This is a speed approaching the speed of light. hence, should the (relativitic) mass of the Alpha particle vary?

marked as duplicate by Gert, John Rennie, Kyle Kanos, user10851, ACuriousMind♦Nov 19 '15 at 0:10

• The relativistic mass increases by a factor of 1.006 compared to its rest mass. $\gamma=\frac{1}{sqrt(1-\frac{v^2}{c^2})}$ – Timeless Nov 18 '15 at 14:16
• No, this is wrong. See comment to answer below. – Gert Nov 18 '15 at 15:12
• BTW, Aman, $10^7\,\mathrm{m/s}$ is about 3% of $c$, so it is mildly relativistic but I would not characterize it as "approaching the speed of light". – dmckee Nov 18 '15 at 15:54

According to the special relativity, there is a formula describing the relation of particle mass with its speed: $$m = {m_0 \over \sqrt {1- ({v \over {c}})^2}}$$ where $m_0$ is the mass of the particle when it is still----rest mass.
So as long as a particle moves, no matter how large or small the velocity is, the mass of the particle $m$ will vary and be different from its rest mass $m_0$.
If $v$ is small, the change in mass is very small. In this case, the ignorance of the change in mass is a good approximation for describing the system you are concerned, that is, back to Newton's world---the mass of a particle is constant. On the other hand, if $v$ is so large that it can be comparable with the speed of light, the change in mass is remarkable. So in this case, we must take the variance of the particle mass into consideration!
• No, this is wrong. Widely believed but nonetheless wrong. It's momentum and kinetic energy that vary relativistically when speed approaches $c$, not mass itself, see: en.wikipedia.org/wiki/Mass_in_special_relativity. – Gert Nov 18 '15 at 15:11