Answer
See the detailed answer below.
Work Step by Step
$$\color{blue}{\bf [a]}$$
To create an energy-level diagram for all $ A = 14 $ nuclei, we need to show the distribution of protons and neutrons. The common $ A = 14 $ isobars are:
$$\text{Carbon ($ ^{14}\text{C} $),$\quad$ Nitrogen ($ ^{14} \text{N} $), $\quad$ Oxygen ($^{14}\text{O}$) } $$
1. Carbon ($^ {14}\text{C}$): It has 6 protons and 8 neutrons.
2. Nitrogen ($^ {14}\text{N}$): It has 7 protons and 7 neutrons.
3. Oxygen ($^{14}\text{O}$) It has 8 protons and 6 neutrons.
See the graphs below.
$$\color{blue}{\bf [b]}$$
1. Nitrogen $ ^{14}\text{N} $ is stable.
2. Carbon $ ^{14}\text{C} $ undergoes beta-minus decay.
3. Oxygen $ ^{14}\text{O} $ undergoes beta-plus decay.
Now we have covered the $ A = 14 $ nuclei: Carbon-14, Nitrogen-14, and Oxygen-14. Only $\underline{\color{red}{\text{ Nitrogen -14 is stable }}}$ among these isotopes.
