The diagram shows an atom of uranium-235 being split into several pieces. What is the name the process shown in the diagram? What is the name of the particles labelled X?

Jan 6, 2017

Here's what I got.

Explanation:

Let's start by identifying the particles labeled $\text{X}$.

As you know, nuclear reactions are characterized by the fact that

• mass is conserved, i.e. the overall mass number of the ractants must be equal to the overall mass number of the products
• charge is conserved, i.e. the overall atomic number of the reactants must be equal to the overall atomic number of the products

Now, notice that you have $1$ particle labeled $\text{X}$ on the reactants' side and $3$ particles labeled $\text{X}$ on the products' side.

Grab a periodic table and look for the atomic numbers of uranium, $\text{U}$, krypton, $\text{Kr}$, and barium, $\text{Ba}$. You will find

• $\text{For U: " -> "atomic number} = 92$

• $\text{For Kr: " -> "atomic number} = 36$

• $\text{For Ba: " -> "atomic number} = 56$

If you take $A$ to be the mass number and $Z$ to be the atomic number of each particle $\text{X}$, you can say that

$\text{_color(darkgreen)(Z)^color(blue)(A)"X" + ""_color(darkgreen)(color(white)(1)92)^color(blue)(235)"U" -> ""_color(darkgreen)(36)^color(blue)(89)"Kr" + ""_color(darkgreen)(color(white)(a)56)^color(blue)(144)"Ba" + 3""_color(darkgreen)(Z)^color(blue)(A)"X}$

Now, you know that mass and charge must be conserved, which means that you can write

$\textcolor{\mathrm{da} r k g r e e n}{Z + 92 = 36 + 56 + 3 Z} \to$ conservation of charge

This will get you

$92 = 92 + 2 Z \implies Z = 0$

You can also write

$\textcolor{b l u e}{A + 235 = 89 + 144 + 3 A} \to$ conservation of mass

This will get you

$2 = 2 A \implies A = 1$

Therefore, you can say that the particle labeled $\text{X}$ is a neutron, since it has no charge and a mass number equal to $1$.

$\text{_Z^A"X" = ""_0^1"n}$

The balanced nuclear equation will look like this

$\text{_ 0^1"n" + ""_ (color(white)(1)92)^235"U" -> ""_ 36^89"Kr" + ""_(color(white)(a)56)^144"Ba" + 3""_0^1"n}$

This nuclear equation describes the nuclear fission of uranium-235.