Question

Write symbolically the nuclear ${\beta }^{+}$ decay process of ${}_6^{11}C$. Is the decayed product X an isotope or isobar of (${}_6^{11}C$)? Given the mass values m (${}_6^{11}C$) = 11.011434 u and m (X) = 11.009305 u. Estimate the Q-value in this process.

Answer 1

${\beta }^{+}$ decay:

${}_{116}C{\to }_{115}X+e^{+}+\nu$

$e^{+}=$ Positron

$\nu =$ Neutrino

As mass number of $C$ and $X$ are the same, $C$ and $X$ are isobars.

Energy released $Q=(m_c-m_x-m_e)c^2$

$=\left[\right(m_c+116m_e)-(m_x+115m_e\left)\right]c^2$

$=[m_c-m_x]c^2$

$=[11.011434-11.009305]c^2$

We have $c^2=931.5MeV/amu$

$=0.002129\times 931.5MeV$

$=1.983$ $MeV$