Identification of massless, chargeless $x$ in a nuclear reaction

Question

On Friday, we had our Physics test. We (the tenth grade students) have the basic introduction to Radioactivity and a few nuclear reactions in our syllabus. In the test, the following question was asked:

Identify $x$ in the following nuclear reaction and state its mass:

$_{12}^{24}Mg + x \rightarrow _{11}^{23}Na + _{1}^{1}H$

Here's what I did:

I noticed that the sum of the masses and atomic numbers of the reactants and products is constant:

Right Hand side (without $x$):
Total sum of mass = 24
Total sum of atomic numbers = 12

Left Hand side:
Total mass = 23 + 1 = 24
Total sum of atomic numbers = 11 + 1 = 12

Since there is no difference in mass or charge, I wrote that $x$ is a massless, chargeless, photon or $\gamma$ particle.

But the source of confusion:

After the test, a few of my friends said the $x$ is an anti-neutrino ($\bar{\nu}$), which is also a massless, chargeless particle. But a $\bar{\nu}$ is released only during the conversion of a neutron right?

$_{0}^{1}n \rightarrow _{+1}^{1}p + _{-1}^{0}e + \bar{\nu}$

How is this applicable in this regard?
Is either of the two answers correct?
If so, which is the right one? If not, what is the correct answer?

Answer 1

You're right that in the context of radioactivity, antineutrinos are pretty much only released when a neutron turns into a proton, ${}_0^1n\to {}_1^1p+{}_{-1}^{\;0}e+\bar{\nu}$. They can also be consumed when a proton turns into a neutron and a positron, ${}_1^1p + \bar{\nu}\to {}_0^1n + {}_{1}^{0}e$. There are some other processes that involve antineutrinos, but they're fairly rare.

But one general rule that applies to all processes in radioactivity is that any reaction that involves a neutrino or antineutrino must also involve the conversion of a proton to a neutron or vice versa.

So think about this: how many protons exist in the initial state? (on the left side of the arrow) And how many neutrons? What about on the right side? Are those numbers the same? That will tell you whether $x$ can be an antineutrino. If it's not an antineutrino, then it has to be a photon, as that is the only other massless, uncharged particle that participates in nuclear reactions.

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Note: technically neutrinos are not massless, but they are so light they might as well be massless when you're talking about radioactivity. They are less than a billionth the mass of a proton.