Question

Suppose that a certain microwave oven has radiation having a wavelength of 11.2 cm.

                        (i) What is the frequency, in s^-1, of this radiation?

                        (ii)What is the wavenumber, in cm^-1, of this radiation?

                        (iii)What is the energy, in J, of a single photon of this radiation?

(iv) How many photons of this light would be required to heat 250.0 mL of water from 22.0^oC to 85.0^oC? Take the density of water as 1.00 g/mL and its specific heat at 4.184 J/(g ^oC).

Answer 1

1. 11.2 cm

i = wavelength * frequency = 3 * 10^8

= 0.112 * frequency = 3 *10^8 ( 11.2 cm or 0.112 m )

= frequency = 3*10^8 / 0.112

= 2.68*10^9 s-1

ii ) wavenumber = 1 / wavelength

= 1 / 11.2

= 0.0893 cm-1

iii ) energy = plank constant * frequency

= 6.626*10^-34 * 2.68*10^9

= 1.78*10^-24 joules

2. mass of water = density * volume

= 1*250 = 250 grams

q = mass * specific heat * change in temperature

= 250 * 4.184 * (85-22)

= 65898 joules

number of photons = energy / energy of one photon

= 65898 / 1.78*10^-24

= 3.7 * 10^28