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Question: Energy of a photon having wave number \(1.00c{m^{ - 1}}\) is A. \(6.62 \times {10^{ - 34}}J\) B....

Energy of a photon having wave number 1.00cm−11.00c{m^{ - 1}} is
A. 6.62×10−34J6.62 \times {10^{ - 34}}J
B. 1.99×10−23J1.99\times {10^{−23}} J
C. 6.62×10−32J6.62\times {10^{−32}} J
D. 6.62×10−36J6.62\times {10^{−36}} J

Explanation

Solution

To solve the above question, we need to know the relationship between the energy of a photon to its wavelength and frequency. By using this relation we can solve the energy of photons. Energy of a photon is the energy carried by each photon.

Complete step by step answer:
From the given data:
λ=1cm−1=0.01m−1\lambda = 1c{m^{ - 1}} = 0.01{m^{ - 1}}
c=3×108ms−1 h=6.625×10−34Js  c = 3 \times {10^8}m{s^{ - 1}} \\\ h = 6.625 \times {10^{ - 34}}Js \\\
By using the energy of photon relation
E=hν ⇒E=hcλ  E = h\nu \\\ \Rightarrow E = \dfrac{{hc}}{\lambda } \\\
Substituting the values for above equation,
E=6.626×10−34×3×1080.01 ⇒E=19.878×10−260.01 ⇒E=1987.8×10−26 ⇒E=1.99×10−23J  E = \dfrac{{6.626 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{0.01}} \\\ \Rightarrow E = \dfrac{{19.878 \times {{10}^{ - 26}}}}{{0.01}} \\\ \Rightarrow E = 1987.8 \times {10^{ - 26}} \\\ \Rightarrow E = 1.99 \times {10^{ - 23}}J \\\

Hence the correct option is B.

Note: It’s very easy to solve this type of question by understanding the photoelectric equation and we should concentrate on the theory of photons. The energy of the photon is directly dependent on its frequency. If greater the energy of a photon then more the frequency. Usually a beam of light consists of many photons such as intensity red light which carry more energy and intensity of blue light which carry less energy.