A particular microwave oven operates at 1000W. The wavelength of the microwave is 12.0cm. You decide that you like your snack to absorb 1.2 x 10^28 photons. For how much time should you have the oven on- with your snack inside of course. Assume 100% efficiency.

I guess I will answer my own question so, if others come across it, it will help

PT/h(lamda)
P: power
T: time (which is the variable in this case)
h: (constant 6.626x10^-34)
c: lamda is found by c/f in which,
c= 3x10^8
frequency= .12 in this case
if you solve accordingly,
t= 19.8 seconds

The frequency of a radiation from your microwave is 120 GHZ. What is the wavelength and energy of the microwave?

To determine how much time you should have the microwave oven on, we need to calculate the total energy required to heat your snack to absorb the given number of photons.

The energy of each photon can be calculated using the formula:

E = hc/λ

Where:
E is the energy of each photon,
h is Planck's constant (6.626 x 10^-34 J*s),
c is the speed of light (3 x 10^8 m/s), and
λ is the wavelength of the microwave.

First, we need to convert the wavelength from centimeters to meters:

λ = 12.0 cm = 12.0/100 m = 0.12 m

Now, we can calculate the energy of each photon:

E = (6.626 x 10^-34 J*s * 3 x 10^8 m/s) / 0.12 m
E ≈ 5.521 x 10^-22 J

Next, we can calculate the total energy required to absorb 1.2 x 10^28 photons:

Total Energy = Energy per photon * Number of photons
Total Energy = 5.521 x 10^-22 J * 1.2 x 10^28 photons
Total Energy ≈ 6.6252 x 10^6 J

Since we assume 100% efficiency, the total energy absorbed by the snack will be equal to the power output of the microwave oven multiplied by the time it is switched on:

Total Energy = Power * Time

Rearranging the equation to solve for time:

Time = Total Energy / Power

Plugging in the known values:

Time = 6.6252 x 10^6 J / 1000 W
Time ≈ 6625.2 seconds

Therefore, you should have the microwave oven on for approximately 6625 seconds (or 1 hour and 50 minutes) to heat your snack to absorb 1.2 x 10^28 photons.