Question

Assume that a neutron breaks into a proton and an electron. What will be the energy released during this process?

Answer 1

Step 1: Given

Neutron $\to$Proton + Electron

Step 2: Known Data

Mass of neutron, $m_n=1.6725\times {10}^{-27}kg$

mass of proton, $m_p=1.6725\times {10}^{-27}kg$

mass of electron, $m_n=9.1\times {10}^{-31}kg$

Step 3: Formula used

Change in mass,$∆m=(m_p+m_e)-m_n$

Energy released, $E=∆m{c}^2$

where c is the speed of light.

Step 4: Calculation

$∆m=(m_p+m_e)-m_n$

$$\begin{gathered} =1.6725\times {10}^{-27}kg+9.1\times {10}^{-31}kg-1.6725\times {10}^{-27}kg \\ =9.1\times {10}^{-31}kg \end{gathered}$$

The energy released during this process,

$E=∆m{c}^2$

$$\begin{gathered} =9.1\times {10}^{-31}kg\times {(3\times {10}^8)}^{2}J \\ =8.19\times {10}^{-14}J \\ =\frac{8.19\times {10}^{-14}}{1.6\times {10}^{-19}\times {10}^6}MeV \\ =0.51MeV \end{gathered}$$

So, energy released during this process will be $8.19\times {10}^{-14}J$or $0.51MeV$.