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During a mock Cambridge interview, one of the questions was about how small a computer could theoretically be.The way I approached it was in terms of what something must be to be considered a computer.

I eventually made some progress, but I made a point that I am quite doubtful about. I said that one can use the photoelectric effect as a timer.

When you shine light on an atom and promote an electron to a higher energy level, there is a time delay before it returns to ground state (or at least there is a time delay between light being absorbed and light being re-radiated), which ought to be constant. I know this point may not really relate to the interview question.

Nevertheless, is what I said true? Is there a (measurable) time delay between the absorption of a photon and the re-radiation of a photon?

lagrange103
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2 Answers2

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Yes excited states have a non-zero lifetime. Electronically excited states of atoms have lifetimes of a few nanoseconds, though the lifetime of other excited states can be as long as 10 million years.

The decay probability can be calculated using Fermi's golden rule. The lifetime is then an average lifetime derived from the decay probability.

The lifetime can be measured directly for long lifetimes, or for short lifetimes by measuring the broadening of the peak in the emission spectrum. If the lifetime is $\tau$ then the uncertainty principle tells us that the energy difference between the excited and ground states is uncertain by around:

$$ \Delta E \approx \frac{\hbar/2}{\tau} $$

This results in a broadening of the emission peak by a frequency of:

$$ \Delta \nu \approx \frac{\Delta E}{h} $$

This is known as lifetime broadening.

John Rennie
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The characteristic time of interaction - energy of interaction relation between two systems is usually written as $\delta E\cdot\delta t\sim\hbar/2$ (do NOT mix with the uncertainty principle). So the characteristic time would be about $\delta t\sim\hbar/(2\delta E)$, where for $\delta E$ we can take the difference of energies between two states.

hayk
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