Question

One molecule of a substance absorbs one quantum of energy. The energy involved when \[1.5\] moles of the substance absorbs red light of frequency \[7.5{\text{ }} \times {\text{ }}{10^{14}}{\text{ }}{\sec ^{ - 1}}\] will be?
A.\[4.49{\text{ }} \times {\text{ }}{10^5}\] J
B.\[2.24{\text{ }} \times {\text{ }}{10^5}\] J
C.\[9.23{\text{ }} \times {\text{ }}{10^7}\] J
D.\[2.24{\text{ }} \times {\text{ }}{10^7}\] J

Answer 1

Hint: One photon carries exactly one quantum of energy and this energy is directly proportional to the frequency of light. It is known that 1 mole of a substance contains \[{{\text{N}}_{\text{A}}}\] number of molecules.
Here, \[{{\text{N}}_{\text{A}}}\] = Avogadro number = \[6.022 \times {10^{23}}\]
Formula used: \[{\text{}E = h\nu }\]
Here, \[{\text{E}}\] = one quantum of energy
\[{\text{h}}\] = Planck's constant
     = \[{\text{6}}{\text{}.626 \times 1}{{\text{0}}^{{\text{ - 34}}}}{\text{Js}}\]
\[{{\nu }}\] = frequency of light

Complete step by step answer:
We know that quantum is the minimum amount of energy associated with the molecule.
Let us first calculate the energy absorbed by the one molecule of substance:
\[{\text{}E = h\nu }\]
By substituting the frequency of red light we get:
\[{\text{E}} = 6.626 \times {10^{ - 34}}\left( {{\text{Js}}} \right){\text{ }} \times {\text{ }}7.5 \times {10^{14}}\left( {{{\text{s}}^{{\text{ - 1}}}}} \right)\]
By multiplying we get energy as:
\[{\text{E}} = 4.9 \times {10^{ - 19}}{\text{ J}}\]
Now, let us calculate energy absorbed by \[1.5\] moles of substance:
We know that 1 mole is equal \[6.022 \times {10^{23}}\] molecules of the substance.
So, \[1.5\] moles will be equal to \[1.5{\text{ }} \times {\text{ }}6.022 \times {10^{23}}\] molecules of the substance.
Which is equal to \[9.033 \times {10^{23}}\] molecules of the substance.
We have calculated energy associated with the 1 molecule of substance now we have to calculate energy associated with \[9.033 \times {10^{23}}\] molecules of the substance.
We know that 1 molecule of substance involves \[4.9 \times {10^{ - 19}}\] Joules of energy.
So, \[9.033 \times {10^{23}}\] molecules of substance will involve \[\left( {4.9 \times {{10}^{ - 19}}} \right) \times \left( {9.033 \times {{10}^{23}}} \right)\] Joules of energy.
Which is equal to \[4.4 \times {10^5}\] Joules of energy.
The value that we got is nearest to the value provided in option A.

Therefore, we can conclude that the correct answer to this question is option A.


Note:
First find the total number of molecules associated with the \[1.5\] moles of substance because we are given the valve of energy associated with the one molecule of the substance and not with the number of moles of substance.