Amodern compact fluorescent lamp contains 1.4 mg of mercury (hg). if each mercury atom in the lamp were to emit a single photon of wavelength 508 nm, how many joules of energy would be emitted?

a. 1.64 j
b. 3.3 j
c. 6.6 x 10^2 j
d. 3.3x10^3 j
e. 4.2 x 10^18 j

A. 1.64 J

Explanation:

First of all, we need to find how many moles correspond to 1.4 mg of mercury. We have:

where

n is the number of moles

m = 1.4 mg = 0.0014 g is the mass of mercury

Mm = 200.6 g/mol is the molar mass of mercury

Substituting, we find

Now we have to find the number of atoms contained in this sample of mercury, which is given by:

where

n is the number of moles

is the Avogadro number

Substituting,

atoms

The energy emitted by each atom (the energy of one photon) is

where

h is the Planck constant

c is the speed of light

is the wavelength

Substituting,

And so, the total energy emitted by the sample is

found in the nucleus

has mass of one amu