Q19 E - College Physics (Urone)

Question

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

Step-by-Step Solution

Answer

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

Step 1: What is atomic mass number ?

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

Step 2: 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

 

Step 3: 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 \(_{25}^{50}M{n_{25}} \to _{24}^{50}C{r_{26}} + {\beta ^ + } + {\nu _c}\).