Animated Solution for Chemistry - s and p-Block Elements: Hydrogen has three isotopes (A), (B) and (C). If the number of neutron(s) in (A), (B) and (C) respectively, are $(x)$, $(y)$ and $(z)$, the sum of $(x)$, $(y)$ and $(z)$ is

Hydrogen is the simplest, lightest, and most abundant element in the universe. It is the fuel of stars and the building block of life. But despite its simplicity, hydrogen holds a fascinating secret: it exists in three distinct isotopic forms.

Imagine you are looking at the atomic structure of hydrogen. Every hydrogen atom must have exactly one proton in its nucleus—that is what defines it as hydrogen. However, the number of neutrons can vary. These variations are what we call isotopes.

Isotopes are atoms of the same element that share the same atomic number ($Z$) but have different mass numbers ($A$). The difference in mass is entirely due to the varying number of neutrons.

Before we dive into the specific isotopes, we need a reliable tool to calculate the number of neutrons.

The mass number ($A$) is the sum of protons and neutrons. Since the atomic number ($Z$) represents the number of protons, finding the neutrons is a simple matter of subtraction:

Keep this master equation in mind as we analyze the three siblings of the hydrogen family.

The Lone Wolf

Let's start with the most common isotope, Protium (${}_1^1\text{H}$). This is the hydrogen we encounter every day in water and organic molecules.

Protium has a mass number of $1$ and an atomic number of $1$. Let's plug these values into our master equation:

Protium has absolutely zero neutrons! It is the only stable isotope in the entire periodic table that consists of just a single proton and an electron. It doesn't need a neutron because there are no other protons in the nucleus to repel it.

The Heavy Lifter

Next up is Deuterium (${}_1^2\text{H}$), often referred to as "heavy hydrogen."

Deuterium has a mass number of $2$ and an atomic number of $1$. Using our formula:

Deuterium contains exactly one neutron. This extra mass makes deuterium twice as heavy as protium. When deuterium combines with oxygen, it forms "heavy water" ($D_{2}O$), which is crucial in nuclear reactors for slowing down fast neutrons.

The Glowing Sibling

Finally, we have Tritium (${}_1^3\text{H}$). Unlike its siblings, tritium is radioactive and highly unstable.

Tritium has a mass number of $3$ and an atomic number of $1$. Let's calculate its neutrons:

Tritium packs two neutrons into its tiny nucleus. This imbalance between protons and neutrons makes the nucleus unstable, leading to beta decay over time.

The problem asks us to find the sum of the neutrons in these three isotopes, represented by $x$, $y$, and $z$.

We have successfully determined the individual values: - $x=0$ (Protium) - $y=1$ (Deuterium) - $z=2$ (Tritium)

Now, let's substitute these values and calculate the final sum:

This question is a beautiful reminder of how fundamental concepts in atomic structure form the bedrock of chemistry. Always remember the unique composition of these three isotopes—they are a favorite among examiners and a cornerstone of chemical science!