Write the given nucleus

The parent nucleus is magnesium: $^{24}_{12}\mathrm{Mg}$

Here,

• Mass number $A = 24$
• Atomic number $Z = 12$

Understand what happens

A hard gamma photon knocks out a proton from the nucleus.

A proton has: $^{1}_{1}p$

So after emission of one proton:

• Mass number decreases by $1$
• Atomic number decreases by $1$

Form the daughter nucleus

$^{24}_{12}\mathrm{Mg} \rightarrow \ ^{23}_{11}X + ^1_1p$

Therefore, $A_X = 24 - 1 = 23$ $Z_X = 12 - 1 = 11$

Element with atomic number $11$ is sodium, Na.

Hence the daughter nucleus is: $^{23}_{11}\mathrm{Na}$

Check the options

• A: the isotope of parent nucleus
  Isotopes have same $Z$ but different $A$. Here $Z$ changes from $12$ to $11$, so this is not an isotope of Mg.

• B: the isobar of parent nucleus
  Isobars have same mass number $A$. Parent has $A=24$, product has $A=23$, so not an isobar of parent.

• C: the nuclide $^{23}_{11}\mathrm{Na}$
  This matches exactly. Correct.

• D: the isobar of $^{23}_{11}\mathrm{Na}$
  Isobars of $^{23}_{11}\mathrm{Na}$ would have $A=23$ but different $Z$. The product is actually $^{23}_{11}\mathrm{Na}$ itself, not its isobar. So incorrect.

Final answer

The nucleus formed is: $^{23}_{11}\mathrm{Na}$

Therefore, the correct option is C.