Question

Be sure to answer all parts. A microwave oven operating at 1.22 × 108 nm is used to heat 165 mL of water (roughly the volume of a teacup) from 37.0°C to 100.0°C. Calculate the number of photons needed if 91.5 percent of microwave energy is converted to the thermal energy of water. × 10 photons

Answer 1

Q water =m*C*(Tf-Ti)

Qwater = 165 * 4.184 * (100-37)

Qw = 43492.68 J

E = hc/WL

h = Planck Constant = 6.626*10^-34 J s

c = speed of particle (i.e. light) = 3*10^8 m/s

E = energy per particle J/photon

WL = wavelength in meters

WL = 1.22*10^8 nm = (1.22*10^8)(10^-9) m = 0.122 m

E = (6.626*10^-34)(3*10^8) /(0.122) = 1.629*10^-24 J/photon

n photons = Etotal / Ephoton = 43492.68 / (1.629*10^-24) = 2.66*10^28 photosn required if 100%

if only 91.% converted

N total = (2.66*10^28)/(0.915) = 2.907*10^28 photons