Suppose the microwave power is $P$, and the absorptance (the depth of the trough in the diagram above) is $f$, where $f = 0$ means no microwaves are absorbed and $f = 1$ means all the microwaves are absorbed. So if we can work out how many photons per second are absorbed this will tell us how many electrons per second are flipped. The electron flips every time a caesium atom absorbs a microwave photon. Then it's just a matter of counting each cycle of your microwave generator, and after 9,192,631,770 of them one second has passed. exactly at the peak of the absorption line. The caesium clock works by tuning the frequency for maximum absorption i.e. Energy is absorbed from the microwaves to flip the electron spin, then the electron either reradiates a photon and relaxes back or it loses the energy and relaxes due to collisions with other caesium atoms. When the microwave frequency is 9,192,631,770 Hz the microwave photons have exactly the right energy to flip the outer electron spin, so at this frequency they are more strongly absorbed than at nearby frequencies. NB not a real spectrum - I drew this as an illustration If you measure the absorption of microwaves by a gas of caesium atoms you'll get a spectrum looking something like this:
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