general chemistry chapter 8

Question

A liquid is exposed to infrared radiation with a wavelength of 4.55×10−4 cm. Assume that all the radiation is absorbed and converted to heat. How many photons are required for the liquid to absorb 22.61 J

 of heat? 

number of photons =

Answer 1

Hello, Sarah,

hv

The energy of a single photon is hv, where h is Plank's constant and v is the frequency of the light.

Plank's constant is 6.626x10^-34 J*sec

We're given the wavelenght, but need the frequency of the light. We can convert wavelength (λ) into frequency (v) by using c = λv, where c is the speed of light at 3x10⁸ m/s.

We need to convert the wavelength given us from cm to meters, by dividing by 100.

(4.55x10^-4cm)*(0.01m/1cm) = 4.55x10^-6 meters

v = (3x10⁸ m/s)/(4.55x10^-6 m) = 6.74x10¹³ sec^-1

Now we can calculate E, the energy of a photon with wavelength 4.55x10^-4 cm:

E = (6.626x10^-34 J*sec)*(6.74x10¹³ sec^-1)

E = 4.47x10^-20 J

It took more energy to calculate than the photon has to offer. I'm returning it once we're finished.

We need enough photos to generate 22.61 J of heat. That would be:

22.61J/(4.47x10^-20J/photon) = 5.06x10²⁰ photons

I went through the calculation quickly, so please check my numbers.

Bob

Answer 2

A liquid is exposed to infrared radiation with a wavelength of 4.55×10−4 cm. Assume that all the radiation is absorbed and converted to heat. How many photons are required for the liquid to absorb 22.61 J

Step1 : Convert wavelength to m

(4.55X10-4cm) x 1m/100cm = 4.55x10-6m

Step 2: Energy in 1 photon of IR radiation at above wavelength = hf = hc/wavelength

1. h is Planck's constant (h = 6.626 x 10^–34 J s),
2. c is speed of IR waves = 3 x10E8 m/s
3. wavelength= 4.55x10-6m

Energy of 1 photon= 4.37E-20 J

4.37E-20 J = 1 photon

22.1 61J = x photons

x photon = 22.61 j/4.37E-20 = 5.17e+20 photons total