Question

The energy of a photon of wavelength k=1 meter is (Planck’s constant=\[6.625\times {{10}^{-34}}\]Js, speed of light=\[3\times {{10}^{8}}\]m/s)
A. $$1.988 \times {10^{ - 23}}$$J
B. $$1.988 \times {10^{ - 28}}$$J
C. $$1.988 \times {10^{ - 30}}$$J
D. $$1.988 \times {10^{ - 25}}$$J

Answer 1

Hint: In this question we will be using Planck Quantum Theory. According to this theory the equation which came out was $E=h\nu $. Here E is known as energy of a particle of light, h is known as the constant factor and v is the frequency .

Complete step by step answer:
So this Planck Quantum Theory states that the energy of a particle of light called photon is directly proportional to the frequency by a constant factor. This means that photons with low frequencies, like radio waves , have lower energies than photons with frequencies, like x- rays.
In this question we will apply this formula
So $E=h\nu $here we will substitute frequency by its other formula that is $\nu =\dfrac{c}{\lambda }$
Now substituting the v in the formula, we get
$E=\dfrac{hc}{\lambda }$
h=\[6.625\times {{10}^{-34}}\]Js
c=\[3\times {{10}^{8}}\]m/s
$\lambda $=1 meter
Now substituting the values in the given formula we get
E=$\dfrac{6.625\times {{10}^{-34}}\times 3\times {{10}^{8}}}{1}$
So
E= \[1.988\times {{10}^{-25}}\]Js.

So, Option D is correct.

Additional information:
Earlier in 1905, Einstein expanded this idea and considered the light itself to be the collection of photons. A photon is the particle which carries the momentum, electromagnetic energy and intrinsic angular momentum. It also carries orbital angular momentum. The photon is a particle which has zero rest mass and travels with a speed of light in vacuum only. The photons which have high frequency have higher energy and vice versa.

Note: Some important points of Planck’s quantum theory are,
(i)The emission or absorption of radiant energy takes place in the form of small packets of energy known as quanta discontinuously.
(ii) Each quantum possesses energy directly proportional to the frequency of the radiation.
(iii)The total number of energy emitted or absorbed by a body is some whole number or integral multiple of quantum.