A particle with rest mass `M_0` , splits up into two identical fragments which fly apart in opposite directions at speeds of 0.90c. Find the rest mass of each fragment.

Answer

`0.218 M_0`

Explanation

Before decaying the particle is at rest and its energy is `epsilon_0=M_(0)c^2` . Since it decays into two identical fragments their total energy must be `epsilon=2mc^2=(2m_0c^2)/(sqrt(1-beta^2))` where `m_0` is the rest mass of a fragment and `u =betac` is its velocity. It follows from the law of conservation of energy that `(2m_0c^2)/(sqrt(1-beta^2))=M_0c^2` whence the rest mass of a fragment is
`m_0=1/2M_0sqrt(1-beta^2)`
Substituting the speed we obtain the rest mass of the fragment.