Particle Physics: Question 4

Worked solution

Part (a): Nuclide notation

Nuclide notation is written as $^{A}_{Z}\text{X}$, with the nucleon number $A$ as a superscript and the proton number $Z$ as a subscript.

• Nuclide 1: $A = 40$, $Z = 19$, so its notation is $^{40}_{19}\text{X}$
• Nuclide 2: $A = 39$, $Z = 19$ (same proton number as Nuclide 1), so its notation is $^{39}_{19}\text{X}$

Part (b): Number of neutrons

The number of neutrons $N$ is found from $N = A - Z$ (nucleon number minus proton number).

• Nuclide 1: $N = 40 - 19 = 21$ neutrons
• Nuclide 2: $N = 39 - 19 = 20$ neutrons

Part (c): Why Nuclide 1 and Nuclide 2 are isotopes

Nuclide 1 and Nuclide 2 both have proton number $Z = 19$. The same number of protons, so they are the same chemical element. However, they have different nucleon numbers (40 and 39), and therefore a different number of neutrons (21 and 20).

Nuclides of the same element (same proton number) with different nucleon numbers are, by definition, isotopes of that element.

Part (d): Is Nuclide 3 an isotope of the same element?

Nuclide 3 has nucleon number $A = 40$, the same as Nuclide 1. However, its proton number is $Z = 20$, which is different from the proton number of Nuclide 1 and Nuclide 2 ($Z = 19$).

Since the defining feature of isotopes is a shared proton number, and Nuclide 3’s proton number is different, Nuclide 3 is not an isotope of the same element. It is a nuclide of a completely different element, even though its nucleon number happens to match that of Nuclide 1.

Final answers

• (a) Nuclide 1 $= \boxed{^{40}_{19}\text{X}}$; Nuclide 2 $= \boxed{^{39}_{19}\text{X}}$
• (b) Nuclide 1 has $\boxed{21}$ neutrons; Nuclide 2 has $\boxed{20}$ neutrons
• (c) Same proton number (19), different nucleon/neutron number, the definition of isotopes.
• (d) No. Nuclide 3 has a different proton number (20), so it is a different element, not an isotope of X.