Write a series of nuclear equations in wTiich Al-27 reacts with a neutron and the product undergoes an alpha decay followed by a beta decay.
So, you know that the first nuclear equation has aluminium-27 react with a neutron.
A neutron has no charge and an atomic mass equal to one, so you can write
27 13Al+10n→28 13Al
The resulting aluminium-28 isotope will then decay via alpha decay.
When isotopes undergo alpha decay, their nucleus emits an alpha particle, which is essentially the nucleus of a helium-4 atom.
Helium-4 has an atomic number equal to 2 and a mass number equal to 4. This means that you can write
28 13Al→AZX+4 2He
Since atomic number and mass number must be conserved in nuclear equations, you get that element X will have
A=28−4=24 and Z=13−2=11
The element that has an atomic number equal to 11 is sodium, Na, which means that you are dealing with the sodium-24 isotope
28 13Al→24 11Na+4 2He
Finally, the sodium-24 isotope undergoes beta decay. In sodium-24's case, it's beta minus, β− decay.
During beta decay, a neutron from the nucleus of the radioactive isotope is converted into a proton. In addition to this, an electron and an electron antineutrino, ¯νe, are emitted by the nucleus.
So, if a neutron is converted into a proton, you can expect the atomic number to increase by 1, but the mass number to remain unchanged.
This means that you have
24 11Na→24 12Y+0-1e+¯νe
The element that has 12 protons in its nucleus is magnesium, which means that the final product of this decay chain is the magnesium-24 isotope.
24 11Na→24 12 Mg+0-1e+¯νe