Answer to Question #116151 in General Chemistry for SOPHIA

Question

Carbon absorbs energy at a wavelength of 150. nm. The total amount of energy emitted by a carbon sample is 1.00x10^5 J. Calculate the number of carbon atoms present in the sample, assuming that each atom emits one photon.

____ atoms

Answer 1

The first thing we need to do is to convert the wavelength to meters. We should remember that 1 meter is 1x10^9 nm so:

∧ = 150 nm / 1x10^9 nm = 1.5x10^-7 m

The formula for Energy in this case is:

E = hc/∧

We already know that c is the speed of light, which is 3x10^8 m/s and h is the planck constant which is 6.63x10^-34 J.s

Replacing data in the above formula:

E = 6.63x10^-34 * 3x10^8 / 1.5x10^-7 = 1.33x10^-18 J per photon.

Now finally to calculate the carbon atoms present in the sample, let's calculate the number of photons:

n° of photons = 1.98x10^5 / 1.33x10^-18

n° of photons = 1.49x10^23 photons

The exercise states that one atom emits on photon, so we can assume that this final result would be the number of carbon atoms present in the sample.