Question

Energy of a quanta of frequency \[{10^{15}}Hz\]and \[h = 6.6 \times {10^{ - 34}}Js\] will be,
A. \[6.6 \times {10^{ - 19}}J\]
B. \[6.6 \times {10^{ - 12}}J\]
C. \[6.6 \times {10^{ - 49}}J\]
D. \[6.6 \times {10^{ - 41}}J\]

Answer 1

Hint:The photon is the qualitative unit of energy of the light wave. It is proportional to the frequency of the light wave. The frequency of the light wave is the most characteristic property because it doesn’t change by changing the medium in which the light is travelling.

Formula used:
\[E = h\nu \]
where h is the Plank’s constant and E is the energy of the photon with a frequency equal to \[\nu \].
\[c = \nu \lambda \]
where c is the speed of light, \[\nu \]is the frequency of the photon and \[\lambda \]is the wavelength of the light wave.

Complete step by step solution:
The energy carried by a single photon is called Photon energy. The quantity of energy which is carried by a photon is directly proportional to the photon's electromagnetic frequency.
When we use the relation between the speed of the photon, frequency and the wavelength then the amount of the energy is inversely proportional to the wavelength.

The higher the photon's frequency, the higher its energy. The frequency of the quanta is given as \[{10^{15}}Hz\]and the value of the Plank’s constant is given as \[6.6 \times {10^{ - 34}}Js\],
\[h = 6.6 \times {10^{ - 34}}Js\]
\[\Rightarrow \nu = {10^{15}}Hz\]
Using the expression for the energy of the photon, we find,
\[E = h\nu \]
Putting the values of Plank’s constant and the frequency, we get
\[E = \left( {6.6 \times {{10}^{ - 34}}} \right) \times \left( {{{10}^{15}}} \right)J\]
\[\therefore E = 6.6 \times {10^{ - 19}}J\]
Hence, the energy of the given photon is \[6.6 \times {10^{ - 19}}J\].

Therefore, the correct option is A.

Note: We must be careful about the units of the physical quantity while solving numerical problems. We need to convert all the given data in standard unit form. The energy of the photon is expressed either in Joule as per S.I unit or in electron-Volt. One electron-Volt is the energy possessed by an electron when it is accelerated through the potential difference of unit volt.