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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 \[7.5 \times {10^{14}}se{c^{ - 1}}\] will be:
A) \[2.99 \times {10^5}J\]
B) \[3.23 \times {10^5}J\]
C) \[4.48 \times {10^5}J\]
D) \[2.99 \times {10^6}J\]

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Last updated date: 14th Jun 2024
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Answer
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Hint: 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 = h\nu $ where,
E= photon energy
h = planck's constant = \[6.626 \times {10^{ - 34}}J\]
$\nu $ = wave frequency.
1 mole = $6.022 \times {10^{23}}$ 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 = h\nu $
h = \[6.626 \times {10^{ - 34}}J\] (Planck’s constant)
frequency = $\nu $= \[7.5 \times {10^{14}}se{c^{ - 1}}\]
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 \[4.96 \times {10^{ - 19}}J\] and this is also equal to the energy absorbed by its 1 molecule.
Calculating the number of molecules in respective moles:
1 mole = $6.022 \times {10^{23}}$ molecules, then
1.5 moles = $1.5 \times 6.022 \times {10^{23}}$ molecules
Now, the energy absorbed by 1 molecule is $5 \times {10^{ - 9}}J$ and by $1.5 \times 6.022 \times {10^{23}}$ 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 \[7.5 \times {10^{14}}se{c^{ - 1}}\]will be $4.52 \times {10^5}J$

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 = 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)