#### Question

Use the same formula you employ in (a) to obtain electron speed for an collector potential of 10 MV. Do you see what is wrong? In what way is the formula to be modified?

#### Solution

Potential of the anode, *V* = 10 MV = 10 × 10^{6} V

The speed of each electron is given as:

`v = (2V e/m)^(1/2)`

`= (2xx10^7 xx 1.76 xx 10^11)^(1/2)`

`= 1.88 xx 10^9 "m/s"`

This result is wrong because nothing can move faster than light. In the above formula, the expression (*mv*^{2}/2) for energy can only be used in the non-relativistic limit, i.e., for*v* << *c*.

For very high speed problems, relativistic equations must be considered for solving them. In the relativistic limit, the total energy is given as:

*E* = *mc*^{2}

Where,

*m *= Relativistic mass

`= m_0 (1 - v^2/c^2)^(1/2)`

*m*_{0} = Mass of the particle at rest

Kinetic energy is given as:

*K* = *mc*^{2} − *m*_{0}*c*^{2}