Question

\({{\rm{\beta }}^{\rm{ + }}}\)decay of \(^{{\rm{52}}}{\rm{Fe}}\)

Short answer

The \({\beta ^ - }\) Decay equation of \(^{52}Fe\)is \(_{26}^{52}F{e_{26}} \to _{25}^{52}M{n_{27}} + {\beta ^ + } + {\nu _e}\).

Step-by-step solution

What is atomic mass number ?

The amount of matter contained in an atom of an element is called its atomic mass.

 Formula to be used

\(A = N + Z\)

Where A is atomic mass number

Z is the number of protons in a nucleus

X is the symbol for the element

In the expression below:

\(_Z^A{X_N}\)

Z is the number of protons in a nucleus

X is the symbol for the element

To determine the  decay equation of \(^{{\rm{52}}}{\rm{Fe}}\)

We know that

\(A = N + Z\)

Where A is atomic mass number

The atomic mass of \(_{26}^{52}{\rm{F}}{{\rm{e}}_{26}}\) is 52 and

\(\begin{align}A &= 52\\Z &= 26\\N &= 26\end{align}\)

Thus,

\(\begin{align}A &= 52\\N &= 26 + 1\\ &= 27\\Z &= A - N\\ &= 52 - 27\\ &= 25\end{align}\)

Therefore, \({\beta ^ - }\) Decay equation of \(^{52}Fe\)is \(_{26}^{52}F{e_{26}} \to _{25}^{52}M{n_{27}} + {\beta ^ + } + {\nu _e}\).