How many photons are in a microwave oven? I have always had trouble connecting the picture of classical electromagnetism with the idea of photons. To make this connection better I'd like to ask the following question. How many photons, at an instant in time, are there inside a microwave while you are heating your food? Since microwaves are so large (~12cm) I figure it could either be one photon or many photons that together form the microwave.
 A: Classical electromagentic waves are characterized by their frequency. They are an emergent state from zillions of photons. Photons are  not waves, they are zero mass elementary point  particles,  characterized by their spin and energy .
The number of photons making up the classical wave can be estimated for specific cases. The energy of an individual photon contributing to the classical wave of frequency $ν$ is  $E=hν$, where h is the Planck constant . The energy of the photons in the microwave range is   is $1.24 µeV$ –> $12.4 feV$ .
If you know the power of your microwave oven, in watts, which are per second, you can get it to electron volts with this calculator and then divide by the energy of a photon for the frequency of your oven.
Try it and you will understand my saying that the classical beam is composed out of zillions of photons.
By the way, the photons do not stay in the oven, they are absorbed and scattered and end up as heat in the food and surroundings.
A: Household microwave ovens operate at 2.45 GHz, apparently.
So the energy of a photons is $E=hf=6.63\times 10^{-34} \times 2.45 \times {10^9}=1.62 \times 10^{-24}$ Joules
So if you take an 800 Watt unit, that is putting $4.92\times 10^{26}$ photons per second into the microwave unit. Which is indeed `many photons'.
(That could be an overestimate by a factor of about 2, depending on whether your '800 Watt' microwave is one that consumes 800 W wall plug power, or one that puts a useful 800 W into the oven. I don't know the exact specification and a quick google search was unhelpful. )  
A: I agree with @RogerJBarlow's calculation arriving at a
production rate of $5\cdot 10^{26}$ photons per second.
However, this doesn't yet answer the question

How many photons, at an instant in time, are there
   inside a microwave?

So let's continue the calculation from here.
Each photon is reflected from the metal walls several
times until it finally is absorbed by the food.
So let's assume it travels around $l=1\text{ m}$
in a zig-zag way.
Using the speed of light ($c=3\cdot 10^8 \text{m/s}$)
this will a take a time of
$$t=\frac{l}{c}=\frac{1\text{ m}}{3\cdot 10^8\text{ m/s}}
=3\cdot 10^{-9}\text{ s}.$$
Hence, we find the number of photons inside the oven: 
$$N=5\cdot 10^{26}{\text{ photons/s}}\cdot 3\cdot 10^{-9}\text{ s}
=1.5 \cdot 10^{18}\text{ photons}.$$
