Question

Calculate energy of one mole of photons of radiation whose frequency is \[5 \times {10^{14}}\] .

Answer 1

Hint: Photons are the quantum of energy but they are specific to light energy. Light and other electromagnetic radiation are quantized and travel in the form of small packets which are called photons and each photon is associated with some energy which is proportional to the frequency at which the radiation travels.

Complete answer:
Max Plank was the first scientist to introduce the concept of quantization of light energy and all other electromagnetic radiations. Before this concept came into existence, light was believed to travel in a continuous fashion.
The smallest packet of energy or quantum that a radiation can have is known as a photon and is associated with a fixed amount of energy irrespective of the source of radiation. The energy is only dependent on the frequency of the radiation or the wavelength associated with it.
One photon contains an energy equal to the product of the Plank’s constant and the frequency associated with the radiation. The formula for energy of a single photon can be written as follows:
\[E = h\nu \]
The value of Plank’s constant is \[6.626 \times {10^{ - 34}}\] and the given value of frequency is \[5 \times {10^{14}}\]
Inserting the values in the above formula, we get
\[E = 6.626 \times {10^{ - 34}}Js \times (5 \times {10^{14}}{s^{ - 1}}) = 3.313 \times {10^{ - 19}}J\]
Since, one mole of photons contains an Avogadro’s number of photons, the total energy can be determined by multiplying the energy of one photon with the Avogadro’s number.
\[E = 3.313 \times {10^{ - 19}}J \times 6.022 \times {10^{23}}mo{l^{ - 1}} = 1.95 \times {10^5}Jmo{l^{ - 1}}\]
\[ \Rightarrow \] Hence, the energy of one mole of photons with frequency \[5 \times {10^{14}}\] is \[1.95 \times {10^5}Jmo{l^{ - 1}}\]

Note:
The energy associated with radiation remains unchanged even if the source changes as long as the frequency or wavelength associated with the radiation remains the same. Particles like electrons tend to show dual character and are therefore discussed as part of matter as well as radiations.