Answer:
A. 1.64 J
Explanation:
First of all, we need to find how many moles correspond to 1.4 mg of mercury. We have:
[tex]n=\frac{m}{M_m}[/tex]
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
[tex]n=\frac{0.0014 g}{200.6 g/mol}=7.0\cdot 10^{-6} mol[/tex]
Now we have to find the number of atoms contained in this sample of mercury, which is given by:
[tex]N=n N_A[/tex]
where
n is the number of moles
[tex]N_A=6.022\cdot 10^{23} mol^{-1}[/tex] is the Avogadro number
Substituting,
[tex]N=(7.0\cdot 10^{-6} mol)(6.022\cdot 10^{23} mol^{-1})=4.22\cdot 10^{18}[/tex] atoms
The energy emitted by each atom (the energy of one photon) is
[tex]E_1 = \frac{hc}{\lambda}[/tex]
where
h is the Planck constant
c is the speed of light
[tex]\lambda=508 nm=5.08\cdot 10^{-7}nm[/tex] is the wavelength
Substituting,
[tex]E_1 = \frac{(6.63\cdot 10^{-34} Js)(3\cdot 10^8 m/s)}{5.08\cdot 10^{-7} m}=3.92\cdot 10^{-19} J[/tex]
And so, the total energy emitted by the sample is
[tex]E=nE_1 = (4.22\cdot 10^{18} )(3.92\cdot 10^{-19}J)=1.64 J[/tex]
