Question

Exposure to high doses of microwaves can cause damage to cells. Estimate how many moles of photons, with λ = 12 cm, must be absorbed to raise the temperature of your eye by 3.0 ºC. Assume the mass of an eye is 11 grams and its specific heat capacity is 4.0 J/g ºC.

Answer 1

11.03 moles of photons, with wavelength of 12 cm, must be absorbed to raise the temperature of your eye by 3.0 ºC.

Step-by-step explanation:

Mass of eye = m = 11 g

The specific heat capacity = c = 4.0 J/g°C

Change in temperature = ΔT = 3.0°C

Heat required to raise the temperature = Q

`Q=mc* \Delta T`

`Q=11g* 4.0* J/g^oC* 3.0^oC=132 J`

Energy of the photon = E

Wavelength of the photon
`\lambda`= 12 cm = 0.12 m (1 cm = 0.01 m)

`E=(hc)/(\lambda )` (Planck's equation)

`E=(6.626* 10^(-34) Js* 3* 10^8 m/s)/(0.01 m)`

`E=1.9878* 10^(-23) J`

`Q=nE`

`n=(Q)/(E)=(132 J)/(1.9878* 10^(-23) J)`

`n=6.6405* 10^(24)`

`1 mole = 6.022* 10^(23) mol^(-1)`

Moles of photons :

`=(6.6405* 10^(24))/(6.022* 10^(23) mol^(-1))`

`=11.03 mol`

11.03 moles of photons, with wavelength of 12 cm, must be absorbed to raise the temperature of your eye by 3.0 ºC.