# Unusual units

This problem set like furlongs per fortnight deals with unusual or what may seem to be less common or seldom used units. The challenge is to convert the astronomers/observers findings into more common units. You may need to locate definitions of either to determine how to setup and solve the problem.

## Problem 1

A farmer has been reading several of the lectures on Wikiversity about radiation astronomy. He has several acres of clover that will not be planted for at least six months. Having become enthusiastic about neutron astronomy he decides to build an acre-sized neutron detector over a one-acre area in a clover field.
Each of his 38 detectors is exactly 100 arshin on a side. He has judiciously designed each so that the direction as well as the energy of each incoming neutron can be determined. He has attached the best pulse-counting electronics he can purchase.
Each detector has been carefully placed level to the ground within 23.3'. But, because his field isn't perfectly level he places his collection of level detectors throughout 1.47 acre-feet.
Each of these detectors has about its own area between itself and the next detector so that some light gets through to grow his clover.
Next, he estimates that his total dedicated detector field samples 64.7 % of the sky over head, which in turn due to local geography is probably not more than 7.63 % of the total celestial sphere.
When he has sufficient power to run the detector, he turns on the array and collects as many neutron counts as possible. Because he has directional determination, neutrons from below the detectors are not counted. During 2 h 12 m 8 s of counting he records a total of 1023 neutrons. At another time later, he counts for 3 h 28 m 16 s and records 4435 neutrons. A third counting period of 1 h 57 m yields 768 neutrons.
From the above information, what is the average neutron flux in neutrons cm$^{-2}$ s$^{-1}$ sr$^{-1}$?
If the average energy of each neutron is 150 MeV, what is the average wavelength in nm?

## Problem 2

The significant other of the farmer in Problem 1 stops by upon occasion and has become interested in neutrons.
She has discovered a unit called a barn. Using the unit she calculates the radius, approximate surface area, and volume of a $^{238}$U nucleus. Calculate these yourself.
As the neutrons in problem 1 are being accelerated through the detector by gravity, what is the neutron pressure over the average surface area of the detector?
What is the neutron pressure in bars?

## Problem 3

How fast are the neutrons going on average as they go through or into the detector?
How fast in knots?
How fast in furlongs per fortnight?

## Problem 4

A hydrogen atom is about 0.11 nm in diameter.
The "relative motion in a hydrogen atom in crossed electric and magnetic fields leads to peculiar quasi-ionized states with an electron localized very far from a proton." Let this peculiar quasi-ionized state be about the diameter of a hydrogen atom.
What is the electric dipole moment of such a hydrogen atom?
If this state or something similar existed within a neutron, what would be the neutron's electric dipole moment?

## Problem 5

If a neutrino is subject to an electric dipole moment formed in the same way as described above for a hydrogen atom, what is the electric dipole moment of a neutrino?
Let a neutrino be on the order of an electron in size; i.e., a radius of 2.8 x 10$^{-15}$ m.
What is the electric dipole moment of a neutrino in Coulomb meters?

## Hypotheses

* Probably the most unusual units are those from around 42,000 b2k.
* History of units and changes through time including pressures for change are doable.