Chapter 30, Problem 24P

To determine

The energy released, when tritium ${}_{\text{1}}{}^3\text{H}$, decays by ${\text{β}}^{\text{-}}$ emission.

Answer to Problem 24P

Solution:

The energy released, when tritium ${}_{\text{1}}{}^3\text{H}$, decays by ${\text{β}}^{\text{-}}$ emission is $0.019\text{MeV}$.

Explanation of Solution

Formula used:

Binding energy is $\Delta m{c}^2$.

Solution:

When ${}_{\text{1}}{}^3\text{H}$ decays by ${\text{β}}^{\text{-}}$ emission, the decay equation is ${}_{\text{1}}{}^3\text{H}\to {}_2{}^3\text{H}\text{e}+{\beta }^{-}$.

Calculation:

Mass of ${}_{\text{1}}{}^3\text{H}$ is $3.016049\text{u}$. Mass of ${}_2{}^3\text{H}\text{e}$ is $3.016029\text{u}$.

Mass defect is $\Delta \text{m}=3.016049\text{u}-3.016029\text{u}=\text{0}\text{.00002}\text{u}$.

Energy released is $\text{0}\text{.00002}\text{u}\times \frac{931.5\text{MeV}}{\text{u}}=0.019\text{MeV}$

Conclusion:

Mass is equivalent to energy. Mass in a decay reaction cannot increase. The change in mass appears as energy.The energy released, when tritium ${}_{\text{1}}{}^3\text{H}$, decays by ${\text{β}}^{\text{-}}$ emission is $0.019\text{MeV}$.