Chapter 1, A Preview of Particle Physics Video Solutions, Quarks And Leptons. An Introductory Course In Modern Particle Physics

Problem 1

Cross sections are often expressed in millibarns, where 1 $\mathrm{mb}=10^{-3} \mathrm{~b}=10^{-27} \mathrm{~cm}^{2}$. Using $\mathrm{GeV}$ units, show that
$$
1 \mathrm{GeV}^{-2}=0.389 \mathrm{mb} \text {. }
$$
So far, we have not considered the elementary charge $e$, which measures how strongly electrons, say, interact electromagnetically with each other. To obtain a dimensionless measure of the strength of this interaction, we compare the electrostatic energy of repulsion between two electrons one natural unit of length apart with the rest mass energy of an electron:
$$
\alpha=\frac{1}{4 \pi} \frac{e^{2}}{(\hbar / m c)} / m c^{2}=\frac{e^{2}}{4 \pi \hbar c} \approx \frac{1}{137}
$$

Ronald Prasad

Numerade Educator

03:32

Problem 2

Show that, in $h=c=1$ units, the Compton wavelength of an electron is $m^{-1}$, the Bohr radius of the hydrogen atom is $(\alpha m)^{-1}$, and the velocity of an electron in its lowest Bohr orbit is simply $\alpha ; m$ is the mass of the electron or, more precisely, the reduced mass $m_{e} m_{p} /\left(m_{e}+m_{p}\right)$.

Guilherme Barros

Numerade Educator

02:45

Problem 3

Justify the statements, that due to the weakness. of the electromagnetic interaction $\left(\alpha \approx \frac{1}{137}\right)$, the hydrogen atom is a loosely bound extended structure and that the nonrelativistic Schrödinger equation is adequate to describe the gross structure of atomic energy levels.

Jeff Vermeire

Numerade Educator