Q18 PE - College Physics (Urone)

Question

\({{\rm{\beta }}^{\rm{ - }}}\) decay of \(^{40}K\) , a naturally occurring rare isotope of potassium responsible for some of our exposure to background radiation.

Step-by-Step Solution

Answer

The \({\beta ^ - }\) Decay equation of \(^{40}K\) is \(_{19}^{40}\;{K_{21}} \to _{20}^{40}\;{K_{20}} + {\beta ^ - } + \overline {{\nu _e}} \).

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= Number of protons in a nucleus

X= symbol for the element

 

In the expression below:

\(_Z^A{X_N}\) 

 

Z = Number of protons in a nucleus

X= symbol for the element

Step 3: To determine the \({{\rm{\beta }}^{\rm{ - }}}\) decay equation of \(^{{\rm{40}}}{\rm{K}}\)

We know that 

\(A = N + Z\)

Where A is atomic mass number

 

The atomic mass of \(_{19}^{40}\;{K_{21}}\) is 40 and

\(\begin{align}A &= 40\\Z &= 19\\N &= 21\end{align}\)

 

Thus,

 

\(\begin{align}N &= 21 - 1\\ &= 20\\Z &= A - N\\ &= 40 - 20\\ &= 20\end{align}\)

 

Therefore, \({\beta ^ - }\) Decay equation of \(^{40}K\) is \(_{19}^{40}\;{K_{21}} \to _{20}^{40}\;{K_{20}} + {\beta ^ - } + \overline {{\nu _e}} \).