Estimate how many microwave photons with 1=12 cm must be absorbed to raise the temperature of your eye by 3 degree C. Assume the mass of an eye is 11 g and its specific heat capacity is 4.0 J/g/k

Is that wavelength of 12 cm?

How much heat is needed to raise the temperature of the eye by 3 C?
That's q = mass eye x specific heat eye x 3 = about 130 J but you need to do it more accurately.

How much energy does each photon have? That's E = hc/wavelength
I estimate about 1.8E-24 J but check that.
Then 1.6E-24J/photon x #photons = 130
Solve for # photons.

To estimate the number of microwave photons required to raise the temperature of your eye, we can use the equation:

Q = m * c * ΔT,

where:
Q is the heat energy required to raise the temperature,
m is the mass of your eye,
c is the specific heat capacity of your eye,
ΔT is the change in temperature.

In this case, we know that:
m = 11 g
c = 4.0 J/g/K (Joules per gram per Kelvin)
ΔT = 3 °C

First, let's convert the temperature change from Celsius to Kelvin:
ΔT = 3 °C = 3 K

Now, let's substitute the values into the equation:
Q = (11 g) * (4.0 J/g/K) * (3 K)
Q = 132 J

We have calculated that 132 Joules of heat energy are required to raise the temperature of the eye by 3 Kelvin.

To estimate the number of microwave photons required, we need to know the energy of each microwave photon. Microwave photons have an energy given by the equation:

E = h * f,

where:
E is the energy of the photon,
h is Planck's constant (approximately 6.626 × 10^-34 J*s),
f is the frequency of the microwave radiation.

We need to find the frequency (f) of the microwave photon with a wavelength (λ) of 12 cm. The speed of light (c) is given by:

c = λ * f,

where:
c is the speed of light,
λ is the wavelength,
f is the frequency.

Rearranging the equation, we have:

f = c / λ.

The speed of light is approximately 3.0 × 10^8 m/s. Converting the wavelength to meters:

λ = 12 cm = 0.12 m.

Now, we can calculate the frequency:

f = (3.0 × 10^8 m/s) / (0.12 m)
f ≈ 2.5 × 10^9 Hz.

Now that we know the frequency, we can calculate the energy of each microwave photon:

E = (6.626 × 10^-34 J*s) * (2.5 × 10^9 Hz)
E ≈ 1.65 × 10^-24 J.

Finally, to estimate the number of microwave photons required to provide 132 Joules of energy, we divide the total energy by the energy of each photon:

Number of photons = Q / E
Number of photons ≈ (132 J) / (1.65 × 10^-24 J).

Evaluating this calculation gives us an extremely large number, approximately 8 × 10^25 photons.

So, approximately 8 × 10^25 microwave photons with a wavelength of 12 cm must be absorbed to raise the temperature of your eye by 3 degrees Celsius.