Exposure to high doses of microwaves can cause tissue damage. Estimate how many photons with a wavelength = 12cm, must be absorbed to raise the temperature of your eye by 3.0 deg C. Assume the mass of the eye is 11g and its specific heat is 4.0 J/gK
7.97x10^25
How much heat energy is needed to raise the T of the eye?
q(in joules) = mass x specific heat x delta T.
How much energy does each photon have?
E(in joules) = hc/wavelength
E/photon x # photons = q
Solve for # photons.
4.17
To estimate the number of photons required to raise the temperature of your eye by 3.0 degrees Celsius, we need to use the formula:
Q = (m * c * ΔT) / N
where:
Q is the energy absorbed by the eye (in Joules)
m is the mass of the eye (in grams)
c is the specific heat of the eye (in J/gK)
ΔT is the change in temperature (in Kelvin)
N is the Avogadro's number (6.02 x 10^23 photons/mol)
First, let's convert the mass of the eye from grams to kilograms:
m = 11g / 1000 = 0.011 kg
Next, let's convert the specific heat of the eye from J/gK to J/kgK:
c = 4.0 J/gK * (1 g / 1000 g) = 0.004 J/kgK
Now, let's convert the change in temperature from Celsius to Kelvin:
ΔT = 3.0°C + 273.15 = 276.15 K
Let's substitute these values into the formula:
Q = (0.011 kg * 0.004 J/kgK * 276.15 K) / N
We know that the wavelength of microwaves is 12 cm, and for photons, the energy is given by the equation:
E = hc / λ
where:
E is the energy of a photon (in Joules)
h is Planck's constant (6.63 x 10^-34 J*s)
c is the speed of light (3.00 x 10^8 m/s)
λ is the wavelength of the photon (in meters)
First, let's convert the wavelength of the microwave to meters:
λ = 12 cm * (1 m / 100 cm) = 0.12 m
Now let's substitute these values into the equation to find the energy of each photon:
E = (6.63 x 10^-34 J*s * 3.00 x 10^8 m/s) / 0.12 m
Once we have the energy of each photon, we can find the number of photons required to deliver the energy Q to raise the temperature of the eye:
N = Q / E
Let's plug in the values and calculate the number of photons required.