At the request of Aiden, the whole team is now practicing how to carry out order of magnitude estimates. We meet every Tuesday from 16:00-17:00 and pick a Purcell problem at random from his series published in the 1980’s called The Back of the Envelope in the American Journal of Physics.
A useful tool for doing these types of calculations is just plain old dimensional analysis and hoping that the unitless factors are of order 1:
- Buckingham Pi theorem: wikipedia article and original article: Phys. Rev. 4, 345 1914
- Percy Williams Bridgman‘s book Dimensional Analysis on the Internet Archive this topic in Chapter IV and much more
Aiden kindly created a single PDF with all of the problems but not the solutions. The solutions can be found by following the doi link in the references below which are clickable.
When I told my Dad about this, he pointed me to this post by Andrew Gelman which links to this 1969 gem titled “Modern Physics From An Elementary Point Of View” by Victor Weisskopf which contains even more problems!
The name Weisskopf comes in many contexts but two important ones include the shape of spectral lines due to collisional broadening which is relevant for probing atoms/molecules in a vapor cell with or without a buffer gas.
In nuclear physics, he published a paper that gives a formula for setting the scale for radiative transition rates for excited nuclei. These rates are often reported in the literature in “Weisskopf units.” A general description of how they are derived and a comparison to experimentally measured transition rates is given here by Leon Van Dommelen. He gives explicit formulas for W.u. depending on the multipole order and character of the transition and has a super-snarky digression on the inconsistencies in the literature for these formulas which I 100% agree with! A beautiful step by step exposition on how to calculate gamma transition probabilities is given by K. Adler and R. M. Steffen as Chapters 1 and 2 in the 1975 book “The Electromagnetic Interaction in Nuclear Spectroscopy” edited by W.D. Hamilton.
Other resources along these lines:
- Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin by Larry Weinstein and John Adam
- Guesstimation 2.0: Solving Today’s Problems on the Back of a Napkin by Larry Weinstein