Level 1: Hydrogen's Electron Moves to Orbit 2: Twice as Long per Lap?
Its magnetic field at the nucleus.
In the Bohr model of hydrogen, the magnetic field produced at the nucleus by the orbiting electron in the first orbit is how many times that in the second orbit?
The orbiting electron acts as a tiny current loop, with current I = e/T, and the field at the centre of a loop is B = μ₀I/2r. Both the current and the radius depend on n.
The field in the first orbit is 32 times stronger: the current there is 8 times larger and the loop is 4 times smaller. Stopping at either factor alone gives the 8 or the 4 option.
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