Silver emits light of 328.1 nm when burned. What is the energy of a mole of these photons?

1 Answer
Simon Moore
Jan 15, 2018

Just under 4 eV

Explanation:

You can use the relationship E=h.ν where E is the energy, h is Planck's constant and ν is the frequency.

However, we do not have frequency, we only have wavelength. So we need to express frequency as follows:

c=ν.λ

ν=cλ

Where c is the speed of light, λ is the wavelength and ν is the frequency.

Therefore you can now say: E=h.cλ

But you need to ensure that your units are consistent. Units of Planck's constant are J.s, speed of light is commonly quoted in m/s, so thats fine. ν is in Hertz which is units of s−1. So again, that ties in OK.

Wavelength, however, is given in nm so in order to ensure that everything balances, you need to express this as metres, (328.1 x 10−9 m).

Now you can work it out:

E=h.cλ

=6.626×10−34.3×108328.1×10−9

= 6.0585×10−19 J

However, as this is a very small amount of energy, it is probably better to express it in units of "electron volts" - one electron volt is 1.602×10−19 J, in which case the answer works out to be 6.0585/1.602 = 3.78 eV.

(One electron volt is the energy involved in the charge of a single electron moving through a potential difference of one volt, and it is a useful unit for expressing extremely small amounts of energy).

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