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Question: One molecule of a substance absorbs one quantum of energy. The energy involved when 1.5 mole of the ...

One molecule of a substance absorbs one quantum of energy. The energy involved when 1.5 mole of the substance absorbs red light of frequency 7.5×1014sec−17.5 \times {10^{14}}se{c^{ - 1}} will be:
A) 2.99×105J2.99 \times {10^5}J
B) 3.23×105J3.23 \times {10^5}J
C) 4.48×105J4.48 \times {10^5}J
D) 2.99×106J2.99 \times {10^6}J

Explanation

Solution

When we transfer the energy, it is not transferred continuously but as discrete packets of energy called quanta.
We can find out the value of this energy by using formula:
E=hνE = h\nu where,
E= photon energy
h = planck's constant = 6.626×10−34J6.626 \times {10^{ - 34}}J
ν\nu = wave frequency.
1 mole = 6.022×10236.022 \times {10^{23}} molecules

Complete step by step answer:
It is given that one molecule of a substance absorbs one quantum of energy whose Formula is given as
E=hνE = h\nu
h = 6.626×10−34J6.626 \times {10^{ - 34}}J (Planck’s constant)
frequency = ν\nu = 7.5×1014sec−17.5 \times {10^{14}}se{c^{ - 1}}
Substituting these values to get energy in one quantum of red light:
E = 6.626 \times {10^{ - 34}} \times 7.5 \times {10^{14}} \\\ E = 4.96 \times {10^{ - 19}}J \\\ E \approx 5 \times {10^{ - 19}}J \\\
Thus, the energy for one quantum of red light is 4.96×10−19J4.96 \times {10^{ - 19}}J and this is also equal to the energy absorbed by its 1 molecule.
Calculating the number of molecules in respective moles:
1 mole = 6.022×10236.022 \times {10^{23}} molecules, then
1.5 moles = 1.5×6.022×10231.5 \times 6.022 \times {10^{23}} molecules
Now, the energy absorbed by 1 molecule is 5×10−9J5 \times {10^{ - 9}}J and by 1.5×6.022×10231.5 \times 6.022 \times {10^{23}} molecules is given as:
E = 5 \times {10^{ -19}} \times 1.5 \times 6.022 \times {10^{23}} \\\ E = 4.52 \times {10^5}J \\\
Therefore, the energy involved when 1.5 mole of the substance absorbs red light of frequency 7.5×1014sec−17.5 \times {10^{14}}se{c^{ - 1}}will be 4.52×105J4.52 \times {10^5}J

Hence option C is correct.

Note: Red light has a wavelength of 700nm, visible light makes up just a small part of the electromagnetic spectrum.
E=hνE = h\nu , this equation is known as the Plank-Einstein relation.
Be very careful about writing the answers in SI units. SI unit of Energy is Joules (J)