← Nuclear Physics

# Nuclear Constituents

Thursday, March 31, 2022

## Historical Postulates

Physicists have historically postulated that the nucleus of an atom contains a certain number of electrons, to balance the nuclear charge of an atom ($+Z$) with the atomic mass number $A$. However, this prediction does not match the experimental results from the nuclear magnetic moment (which shows that protons have spin $1/2$).

## Neutrons

The neutron was discovered as an nuclear constituent in 1932. In the proton-neutron model, atoms of atomic number $Z$ have $Z$ protons and $A-Z$ neutrons, such that the atomic mass number is $A$. Chemical properties of an element depend only on the atomic number $Z$.

Name Symbol Charge Mass Rest energy Spin
Proton $p$ $+e$ $1.007276~\text{u}$ $938.28~\text{MeV}$ $\frac{1}{2}$
Neutron $n$ $+0$ $1.008665~\text{u}$ $939.57~\text{MeV}$ $\frac{1}{2}$

### Isotopes

Atoms of the same atomic number with different mass numbers are called isotopes. Isotopes with atomic number $Z$, mass number $A$, and neutron number $N$ ($N=A-Z$) are written as

$^A_ZX_N$

Since $X$ (a chemical symbol) and $Z$ hold the same information, $Z$ is not necessary. And with both the atomic number and mass number, $N$ is not necessary. Therefore, isotopes are compactly written as $^1H$, $^2H$, etc.