Question

\({{\rm{\beta }}^{\rm{ + }}}\)decay of \(^{{\rm{50}}}{\rm{Mn}}\)

Short answer

The \({\beta ^ - }\) Decay equation of \(^{50}Mn\) is \(_{25}^{50}M{n_{25}} \to _{24}^{50}C{r_{26}} + {\beta ^ + } + {\nu _c}\).

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 \(^{{\rm{50}}}{\rm{Mn}}\)

We know that

\(A = N + Z\)

Where A is atomic mass number

The atomic mass of \(_{25}^{50}M{n_{25}}\) is 50 and

\(\begin{align}A &= 50\\Z &= 25\\N &= 25\end{align}\)

Thus,

\(\begin{align}A &= 50\\N &= 25 + 1\\ &= 26\\Z &= A - N\\ &= 50 - 26\\ &= 24\end{align}\)

Therefore, \({\beta ^ - }\) Decay equation of \(^{50}Mn\) is \(_{25}^{50}M{n_{25}} \to _{24}^{50}C{r_{26}} + {\beta ^ + } + {\nu _c}\).