Question

Physicists need a convenient unit to state the size of an atomic nucleus. In which unit are nuclear sizes usually expressed?

Hint:

The unit is named after Enrico Fermi and equals 10^-15 metres.

Answer 1

Nuclear sizes are usually expressed in a unit called the fermi, where 1 fermi equals \(10^{-15}\) metres.

Step 1: The problem with using metres.
Atomic nuclei are extraordinarily small, with typical radii of a few times \(10^{-15}\) m. Writing distances this small using the metre directly would require many zeros after the decimal point, which is inconvenient and error prone.

Step 2: The chosen unit.
To avoid this, physicists use the fermi (symbol fm), named after the nuclear physicist Enrico Fermi. It is defined so that \(1\ \text{fermi} = 10^{-15}\) m, matching the natural scale of nuclear radii.

Step 3: Typical values.
For example, the radius of a proton is close to 0.8 to 1 fermi, and for a medium sized nucleus the radius can be estimated using the formula \(r = r_0 A^{1/3}\), where \(r_0 \approx 1.2\) fermi and A is the mass number.

Step 4: Answer.
So nuclear sizes are expressed in fermis, a unit specifically suited to the extremely small scale of the atomic nucleus.