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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:

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

The impulse imparted to the shells equals the change in the momentum:
Fav*(Delta t)= Delta m*v.
The mass change is
Delta m= n*m= (89.9shells)*(88.7g)=7.97Kg
So the average force is
F=((v)*(Delta m))/t= ((929)*(7.97))/4.84=1529.78 N
Since the velocity of the shells is much greater than the velocity of the helicopter, there is no need to use relative velocity.