Animated Solution for Chemistry - s and p-Block Elements: The total number of isotopes of hydrogen and number of radioactive isotopes among them, respectively, are

Imagine the vast, sprawling cosmos. The most abundant and fundamental building block of this universe is hydrogen. It is the very first element on our periodic table, boasting an atomic number of $Z=1$. This means that at its core, a standard hydrogen atom has just a single, solitary proton.

But nature loves variety. Even the simplest element has a few tricks up its sleeve. This brings us to the fascinating concept of isotopes.

Think of isotopes like siblings in a family. They share the same last name and the same fundamental identity, but they might have different weights. In the atomic world, isotopes of an element have the exact same number of protons (which defines their chemical identity) but a different number of neutrons.

Because neutrons carry mass but no electrical charge, adding or removing them changes the atomic mass ($A$) of the atom without changing its atomic number ($Z$).

Hydrogen is incredibly unique in the periodic table because its isotopes are so distinct that they actually have their own special names. Let's meet the family:

1. Protium (${}_1^1\text{H}$): This is the most common sibling. It has $1$ proton and absolutely $0$ neutrons. It is the lightest and most abundant form of hydrogen in the universe.

2. Deuterium (${}_1^2\text{H}$): The middle sibling. It has $1$ proton and $1$ neutron. Because it has twice the mass of Protium, it is often called "heavy hydrogen." It is famously used to make "heavy water" ($D_{2}O$), which acts as a moderator in nuclear reactors.

3. Tritium (${}_1^3\text{H}$): The heaviest sibling. It packs $1$ proton and $2$ neutrons into its tiny nucleus.

If we tally them up, we can clearly see that hydrogen has exactly three naturally occurring isotopes: Protium, Deuterium, and Tritium.

Radioactivity

Now, out of these three, one of them is a bit of a rebel. It is unstable and radioactive. But which one, and why?

The answer is Tritium.

To understand why Tritium is radioactive, we have to look at the delicate balancing act happening inside the nucleus. The nucleus is a battleground between two fundamental forces: the repulsive electromagnetic force (which makes positively charged protons want to fly apart) and the attractive strong nuclear force (which is provided by both protons and neutrons to hold the nucleus together).

The Neutron-to-Proton Ratio

For light elements, the ideal ratio of neutrons to protons ($n/p$) for a stable nucleus is exactly $1$. Let's calculate this ratio for our hydrogen family:

- Protium: $n/p=0/1=0$ (Stable, as it's just a single proton with no repulsive forces to overcome). - Deuterium: $n/p=1/1=1$ (Perfectly stable). - Tritium: $n/p=2/1=2$ (Highly unstable).

For a light element like hydrogen, an $n/p$ ratio of $2$ is simply too high. The nucleus has too much nuclear energy and becomes unstable. To find stability, Tritium undergoes radioactive decay, specifically emitting low-energy beta particles (${\beta }^{-}$) to correct its neutron-to-proton imbalance.

Bringing our entire thought process together: the total number of hydrogen isotopes is $3$, and exactly $1$ of them (Tritium) is radioactive.

Therefore, the correct answer is $3$ and $1$.