Answer to Question #330428 in General Chemistry for leo

Question

7. Carbon absorbs energy at a wavelength of 150.0 nm. The total amount of energy emitted by a carbon sample is 1.98 x 105 J. Calculate the number of carbon atoms present in the sample, assuming that each atom emits one photon.

Answer 1

The first thing we need to do is to convert the wavelength to meters. We should remember that 1 meter is 1×10⁹ nm so:

$\lambda$ = 150 nm / 1×10⁹ nm = 1.5×10^-7 m

The formula for Energy in this case is:

E = hc/$\lambda$

We already know that c is the speed of light, which is 3×10⁸ m/s and h is the planck constant which is 6.63×10^-34 J s

Replacing data in the above formula:

E = 6.63×10^-34 × 3×10⁸ / 1.5×10^-7 = 1.33×10^-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 = 1.98×10⁵ / 1.33×10^-18

N of photons = 1.49×10²³ 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.