# Heating 235g of water from 22.6 C to 94.4 C in a microwave requires 7.06 X 10^4 J. If the microwave frequency is 2.88X10^10/s, how many electromagnetic quanta are required to supply the required...

Heating 235g of water from 22.6 C to 94.4 C in a microwave requires 7.06 X 10^4 J.

If the microwave frequency is 2.88X10^10/s, how many electromagnetic quanta are required to supply the required 7.06 X10^4 Joules?

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Planck's relation is the formula which links the energy in Joules(E) of a photon with its frequency in Hertz (v) through Planck's Constant(`h=6.626*10^-34 J*S` ).

`E=hv`

As a photon is a quantum of electromagnetic energy, we can calculate the energy of a single quantum by plugging in the value above and looking up Planck's Constant.

`E=hv~~(6.626*10^-34)*(2.88*10^10)=1.9083*10^-23`

Now we know the energy of a single quantum, it's simple to calculate the number of quanta required to have `7.06*10^4` Joules.

If we call `E_t` the total energy required and `E_p` the energy of a single photon, then the number of quanta required, n, is calculated using the formulae

`E_t=nE_p`

`n=E_p/E_t=hv/E_t~~((6.626*10^34)*(2.88*10^10))/(7.06*10^4)=2.703*10^40`

We are going to use Plack Formula: E=nhf

E is energy, n is the number of quanta, h is the Plank's conant (6.626x10^-34 Js) and f is the frequancy of the radiation. We can write the Plank equation for our "arget Variable" as:

n=E/hf

Putting all values:

n=(7.06 X10^4 J)/(6.626x10^-34 Js * 2.88X10^10 /s)

= 3.6996x10^27 quanta.