2813Al
Explanation:You know that alpha decay takes place when a α-particle is being ejected from the nucleus of a radioactive isotope.An
α-particle is simply the nucleus of a helium-4 atom. A helium-4 atom has a total of two protons and two neutrons in its nucleus, and two electrons surrounding that nucleus.
In that case, if a α-particle is the nucleus of a helium-4 atom, then it must have a mass number equal to 4, since it has two protons and two neutrons, and a net charge of (2+) since it no longer has the two electrons that the helium-4 atom has.
So, you know that an unknown radioactive isotope decays via alpha decay to yield a sodium-24 nucleus.
A sodium-24 nucleus contains 11 protons and 13 neutrons. This means that you can write
AZX→2411Na+42α
Here A and Z represent the unknown element's mass number and atomic number, respectively.
So, if you take into account the fact that mass number and atomic number must be conserved in a nuclear reaction, you can say that
A=24+4 and Z=11+2
The unknown isotope will thus have
{A=28Z=13
A quick look at the periodic table will show you that the element that has 13 protons in its nucleus is aluminum, Al. This means that you're dealing with aluminum-28, an isotope of aluminum that has 15 neutrons in its nucleus.
The complete nuclear equation will be
2813Al→2411Na+42α
