Light in the infrared portion of the electromagnetic spectrum excites vibrations of certain molecules, causing them to move more rapidly.

Question

Light in the infrared portion of the electromagnetic spectrum excites vibrations of certain molecules, causing them to move more rapidly. In this manner, infrared light can be used to heat a substance. If a 1000.-mW, 808-nm laser is used to heat a 50.0-mL sample of water from 22.0 o C to its boiling point,

a) How many photons will the water absorb?

b) What is the minimum amount of time this will take?

Answer 1

a). First, find the amount of heat energy needed to raise the temperature of the water to its boiling point.

q = mC∆T

q = (50 g)(4.184 J/gº)(78º) = 16,318 J

Next, find the energy provided by the 808 nm laser.

E = hc/λ

E = (6.626x10^-34 Js)(3x10⁸ m/s)(808x10^-9 m) = 2.46x10^-19 J

This is the energy PER photon

Find number of photons needed.

16,318 J x 1 photon / 2.46x10^-19 J = 6.63x10²² photons needed

b). To find the time it will take, use the fact that 1 W = 1 J/sec = 60 J/min

1 W = 60 J / min

1000 mW x 1 W / 1000 mW = 1 W = 60 J / min

16,318 J x 1 min / 60 J = 1939 minutes

Converting this to hours we have 1939 min x 60 hrs / min = 32.3 hours = minimum time needed