Question

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

Answer 1

Hint:
The particle-like packets of light containing energy, charge or momentum is called photons, a term also applicable to quanta. A photon is said to be a quantum of light. A quanta is a minimum amount of any physical entity involved in an interaction.

Complete step by step answer:
Energy of red light $ = 7.5 \times {10^{14}}{\sec ^{ - 1}}$
(As given in the question)
Energy of one quantum of red light is .
$ = 6.626 \times {10^{ - 34}} \times 7.5 \times {10^{14}}$
$ = 4.9 \times {10^{ - 19}}J$
Numbers of molecules in $1{\text{ mole = 6}}{\text{.022}} \times {10^{23}}$
Energy absorbed by $1{\text{ }}\operatorname{molecule} \approx 5 \times {10^{ - 19}}J$
We know that,
1 mole contains ${\text{ = 6}}{\text{.022}} \times {\text{1}}{{\text{0}}^{23}}$ molecules.
So $1.5$ mole contains ${\text{ = 1}}{\text{.5}} \times {\text{6}}{\text{.022}} \times {10^{23}}$ molecules.
So energy absorbed by $1.5 \times 6.022 \times {10^{23}}$ molecules.
$ = 4.9 \times {10^{ - 19}} \times 6.022 \times {10^{23}} \times 1.5$
$ = 4.4 \times {10^5}J$
Hence, (A) option is the correct one.

Additional Information:
-The quantization of energy refers to the fact that at subatomic levels, energy is best thought of as occurring in discrete ‘packets’ called photons.
-Photons are packages of energy and correspond to different types of electromagnetic radiation.
-The formula is $E = hf$ where $E$ is energy $f$ is frequency and $h$ is ting constant called planck's constant $\left( {6.62 \times {{10}^{ - 36}}\dfrac{{{m^2}kg}}{{\sec }}} \right)$
-This constant regulates and quantized the energy of the universe.

Note: Light is wave, it nevertheless exists in discrete (distinct, countable and indivisible) units i.e. particles. Light is made up of photons. That’s why it means that light is quantized.