The photon of hard gamma radiation knocks a proton out of $$^{24}_{12}$$Mg nucleus to form

The parent nuclide is $$^{24}_{12}\text{Mg}$$ (magnesium-24). It contains

• atomic number $$Z = 12$$  (protons)
• mass number $$A = 24$$  (protons + neutrons)

A hard $$\gamma$$-ray photon can eject a proton from the nucleus. When exactly one proton leaves the nucleus:

• The atomic number decreases by one, because the nucleus has one proton less:
$$Z_{\text{new}} = 12 - 1 = 11$$

• The mass number also decreases by one, because that proton carries away one unit of mass number:
$$A_{\text{new}} = 24 - 1 = 23$$

Hence the residual nucleus is $$^{23}_{11}\text{X}$$, where $$Z = 11$$ corresponds to the element sodium (Na). Therefore the product nucleus is $$^{23}_{11}\text{Na}$$.

Now check the character of this product:

Isotopes have the same $$Z$$ (not true, 12 ≠ 11).
Isobars have the same $$A$$ (not true, 24 ≠ 23).
Thus neither Option A nor Option B fits.

The nucleus obtained is precisely $$^{23}_{11}\text{Na}$$, matching Option C. Option D is wrong because “an isobar of $$^{23}_{11}\text{Na}$$” would need $$A = 23$$ but a different $$Z$$.

Hence,

Option C which is: the nuclide $$^{23}_{11}\text{Na}$$