Question

A particular microwave oven delivers 750 watts (exact value). (A watt is a unit of power, which is the joules of energy delivered, or used, per second.) If the oven uses microwave radiation with a wavelength of 12.6 cm, how many photons of this radiation are required to heat 1.00 g of water by 1.00 °C, assuming that all of the photons are absorbed? The specific heat of water is 4.184 J / g•°C at 25°C.

Answer 1

1) determine the Joules of energy necessary to heat the water:

q = (mass) Δt) (C_p)

q = (1.0 g) (1 °C) (4.184 J g^-1 °C^-1)

q = 4.184 J

2) to determine how many Joules are carried by one photon of wavelength 12.6 cm:

Using λν = c and E = hν,

(12.6 cm) (ν) = 3.00 x 10¹⁰ cm s^-1

ν = 2.381 x 10⁹ s^-1

E = (6.626 x 10^-34 J s) (2.381 x 10⁹ s^-1)

E = 1.578 x 10^-24 J per photon

3) Determination of moles of photons required:

4.814 J / 1.578x 10^-24 J per photon = 3.0507 x 10²⁴ photons

3.0507 x 10²⁴ photons / 6.022 x 10²³ photons mol^-1 = 5.066 moles of photons