A nuclear reaction is described by the equation below. Identify the particle 𝑋.
The nuclear reaction equation uses nuclide notation to represent the entities. The letter or letters in the middle are the symbol for the element or particle. The number to the bottom left is the atomic number, otherwise known as the proton number. The atomic number is equal to the number of protons in that entity. The number to the top left is the mass number. The mass number is equal to the number of protons plus the number of neutrons in that entity.
For example, for the second entity in the reaction equation, the symbol U indicates uranium. The number 92 in the bottom left indicates that it has 92 protons. And the number in the top left, 235, indicates that there are 235 nucleons. Nucleons are either protons or neutrons. The symbol for a neutron is 𝑁. So, the first entity in the equation is a neutron. A neutron has an atomic number of zero. So, there are no protons.
What about the number of neutrons? Well it makes sense that a neutron is one neutron. But for other entities where this is less obvious, we can calculate the number of neutrons by taking away the atomic number from the mass number, taking away the number of protons from the number of protons plus the number of neutrons. The second entity is uranium-235. It has 92 protons because it has an atomic number of 92. And it has 143 neutrons, which is equal to 235 minus 92. The third entity in this equation is krypton-92, with 36 protons and 56 neutrons.
As of yet, we don’t know the atomic number or the mass number of our unknown 𝑋. So I’ll label the number of protons 𝑍 and the number of neutrons 𝑁. And for our last entity, three neutrons, we have zero protons and three neutrons. Now, in this reaction, the numbers of protons and neutrons are conserved. We know this because there’s no beta emission. No beta minus or beta plus particles have been released. So we don’t have any neutrons turning into protons or protons turning into neutrons. So the number of protons in the reactants and the number protons in the products are the same. And the number of neutrons in the reactants and the number of neutrons in the products are the same.
So ignoring the zeros, our first equation is that 92 is equal to 36 plus 𝑍. So 𝑍 is equal to 92 minus 36. So 𝑍 is equal to 56. Now, for the neutrons, one plus 143 is equal to 56 plus 𝑁 plus three. So 𝑁 is equal to one plus 143 minus 56 minus three, which is 85. Our mass number, 𝐴, is equal to 𝑍 plus 𝑁. So the mass number of our unknown, 𝑋, is 141.
The last thing we need to do is look up the chemical symbol on the periodic table, the one with atomic number 56. That’s barium, with symbol Ba. So our mystery particle 𝑋 is a barium isotope with mass number of 141, which is otherwise known as barium-141. That’s an entity with 56 protons, 85 neutrons, and, therefore, a mass number of 141. Be careful not to use the number of neutrons in place of the mass number.