Amicrowave oven operating at 1.22 × 108 nm is used to heat 165 ml of water (roughly the volume of a teacup) from 23.0°c to 100.0°c. calculate the number of photons needed if 88.3 percent of microwave energy is converted to the thermal energy of water.

The number of photons are

Explanation:

We are given:

Wavelength of microwave =    (Conversion factor:    )

To calculate the energy of one photon, we use Planck's equation, which is:

where,

h = Planck's constant =

c = speed of light =

= wavelength = 0.122 m

Putting values in above equation, we get:

Now, calculating the energy of the photon with 88.3 % efficiency, we get:

To calculate the mass of water, we use the equation:

Density of water = 1 g/mL

Volume of water = 165 mL

Putting values in above equation, we get:

To calculate the amount of energy of photons to raise the temperature from 23°C to 100°C, we use the equation:

where,

m = mass of water = 165 g

c = specific heat capacity of water = 4.184 J/g.°C

= change in temperature =

Putting values in above equation, we get:

This energy is the amount of energy for 'n' number of photons.

To calculate the number of photons, we divide the total energy by energy of one photon, we get:

q = 53127.72 J

E =

Putting values in above equation, we get:

Hence, the number of photons are

The answer is going to be c

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