Q17 PE - College Physics (Urone)

Question

\({{\rm{\beta }}^{\rm{ - }}}\) decay of \(^{\rm{3}}{\rm{H}}\) (tritium), a manufactured isotope of hydrogen used in some digital watch displays, and manufactured primarily for use in hydrogen bombs  

Step-by-Step Solution

Answer

The \({\beta ^ - }\) Decay equation of \(_1^3{H_2}  is  {\rm{}}_1^3{H_2} \to _2^3H{e_1} + {\beta ^ - } + \overline {{\nu _e}} \).

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 \(^{\rm{3}}{\rm{H}}\)

We know that 

\(A = N + Z\)

Where A is atomic mass number

 

The atomic mass of \(_1^3{{\rm{H}}_2}\) is 3 and

\(\begin{align}A &= 3\\Z &= 1\;\\N &= 2\end{align}\)

 

An electron and an antineutrino are released as a result of Beta decay.

\(\begin{align}A &= 3\\N &= 1 - ( - 1) = 2\\Z &= A - N\\ & = 3 - 2\\ &= 1\end{align}\)

As charge on beta particle is negative, so \({\beta ^ - }\) Decay equation of \(_1^3{H_2}{\rm{ is }}_1^3{H_2} \to _2^3H{e_1} + {\beta ^ - } + \overline {{\nu _e}} \)

 

Therefore, \({\beta ^ - }\) Decay equation of \(_1^3{H_2}{\rm{ is }}_1^3{H_2} \to _2^3H{e_1} + {\beta ^ - } + \overline {{\nu _e}} \).