Chapter 26, Problem 59GP

To determine

The energy required to break the electron.

Answer to Problem 59GP

  $\text{28}\text{.3}\text{MeV}$

Explanation of Solution

Given:

Rest mass of proton is $\text{1}\text{.00783}\text{u}$

Rest mass of neutron is $\text{1}\text{.00867}\text{u}$

Rest mass of Helium is $\text{4}\text{.00260}\text{u}$

Formula used:

The binding energy is the energy required to provide the increase in rest mass

  $E=\left[\left(2m_p+2m_n\right)-m_{He}\right]c^2$

Where,

  $E$ is energy

  $m_p$ is rest mass of proton

  $m_n$ is rest mass of neutron

  $m_{He}$ is rest mass of helium

  $c$ is speed of light, $3.00\times {10}^{8}m/s$

It is known that one atomic mass unit, $1u=931.5MeV/c^2$

Calculation:

By substituting all the values:

  $KE=\left[2\left(1.00783u\right)+2\left(1.00867u\right)-m_{He}4.00260u\right]c^2\left(\frac{931.5MeV}{u{c}^2}\right)=28.3MeV$

Conclusion: The required value is $28.3MeV$ .