# Why $1 \ \mathrm{fm}$ is often used in modern physics?

In the International System, we all know that a one femto (or one Fermi) is equal to

$$1 \ \mathrm{fm}=10^{-15} \ \mathrm{m}$$

What is the historical reason why this unit of measure was adopted as a submultiple of the meter? Why is this value often used in modern physics?

• I've removed a comment discussion that seems to have resolved itself. We are always happy to discuss community-building and communication issues in Physics Chat or on Physics Meta.
– rob
Oct 6 '19 at 20:44

## 1 Answer

What is the historical reason why this unit of measure was adopted as a submultiple of the International System?

The SI prefixes denote factors of ten (deci, deka), hundred (centi, hecto), and thousand (milli, kilo). Beyond that, the prefixes go in steps of 1000. According to the wikipedia article, micro- ($$10^{-6}$$) dates to 1873; nano- and pico- ($$10^{-9}$$ and $$10^{-12}$$) date to 1960; femto- and atto- ($$10^{-15}$$ and $$10^{-18}$$) date to 1964; and zepto- and yocto- ($$10^{-21}$$ and $$10^{-24}$$) date to 1991.

Why is this value often used in modern physics?

It so happens that the effective radius of a proton or neutron is something like 1.2--1.4 femtometer. This is related to the range parameter of the pion-mediated Yukawa-type residual strong force that holds nuclei together, $$r_0 = \hbar c / m_\pi c^2$$, where the pion mass is $$m_\pi c^2 \approx 140\rm\,MeV$$. I suspect that the name "fermi" became common among nuclear physicists as the field developed in the 1930s and 1940s, in recognition of the important contributions of Fermi, and that the "f" in "femto-" was chosen in 1960 in concordance with that tradition.

• I have been told (here in Sweden) that femto- comes from the Swedish "femton" which means 15.
– user137289
Oct 6 '19 at 20:39
• In a letter to Cern Courier in 2000, physicist Dave Jackson from Berkeley attributed the femto prefix to Leon Rosenfeld (1904-1974): "It was Leon Rosenfeld in Copenhagen who got femto put on. Femten is the number fifteen in Danish." Oct 7 '19 at 7:10