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Mass number and symbols

Radiation and the atom · level 4, lesson 5 of 6

A question to start

Scientists write uranium-238 as \(^{238}_{92}\text{U}\). What do the two numbers tell you?

The idea

Two numbers describe a nucleus:

  • The atomic number \(Z\): the number of protons. It decides the element.
  • The mass number \(A\): the number of protons plus neutrons.

So the number of neutrons is \(N = A - Z\).

A nuclear symbol writes the mass number at the top left and the atomic number at the bottom left: \(^{A}_{Z}\text{X}\), where X is the element's symbol. Because protons and neutrons each weigh about 1 atomic mass unit (u), the mass number is close to the atom's mass in u.

Isotope Symbol Protons Neutrons
Carbon-14 \(^{14}_{6}\text{C}\) 6 8
Potassium-40 \(^{40}_{19}\text{K}\) 19 21
Argon-40 \(^{40}_{18}\text{Ar}\) 18 22
Uranium-238 \(^{238}_{92}\text{U}\) 92 146
C146 mass numberatomic numberprotons + neutrons = 14protons = 6so neutrons = 8

Worked examples

1. Uranium-238. \(Z = 92\), \(A = 238\), so \(N = 238 - 92 = 146\) neutrons.

2. Same mass number, different element. Potassium-40 and argon-40 both have \(A = 40\). Potassium has 19 protons and argon 18. When a potassium-40 nucleus breaks down, it can turn into argon-40. That is how rocks are dated (level 8).

3. Argon on Earth. NIST gives Earth's argon as 99.60% argon-40, 0.33% argon-36 and 0.06% argon-38. Most of it is argon-40, made over billions of years by potassium-40 breaking down in rocks.

Try it

  1. What is the mass number?
  2. How many neutrons are in \(^{56}_{26}\text{Fe}\)?
  3. Write the symbol for oxygen-16 (oxygen has 8 protons).
  4. Argon-36 and argon-40: which has more neutrons, and by how many?
Answers
  1. The number of protons plus neutrons in the nucleus.
  2. \(56 - 26 = 30\).
  3. \(^{16}_{8}\text{O}\).
  4. Argon-40, by 4 (22 neutrons against 18).

Common mistake

Subtracting the wrong way. The neutrons are \(A - Z\), the big number minus the small one. \(Z - A\) would give a negative number of neutrons.

Where it leads