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Question: Calculate the approximates energy of a photon given that wavelength of photon is 2 nm and Planck con...

Calculate the approximates energy of a photon given that wavelength of photon is 2 nm and Planck constant h\mathrm{h} is 6.6×10−34 J s6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}.
A.4×10−51 J 4\times {{10}^{-51}}~\text{J }
B.1×10−34 J1 \times 10^{-34} \mathrm{~J}
C.1×10−16 J1\times {{10}^{-16}}~\text{J}
D. 1×1034 J1 \times 10^{34} \mathrm{~J}

Explanation

Solution

The photon's energy is inversely proportional to the wavelength and, therefore, directly proportional to the frequency. This is because they are inversely proportional to each other in wavelength and frequency. Calculate the energy of a photon and then, to calculate the number of photons, you use the total energy.
Formula used:
E=hv=hcλ\mathrm{E}=\mathrm{h} v=\dfrac{\mathrm{hc}}{\lambda}

Complete answer:
For a calculation of the energy of a photon, see How to calculate the energy of an electromagnetic radiation photon. The constant of Planck, or the constant of Planck, is the quantum of electromagnetic action which relates the energy of a photon to its frequency. The Planck constant multiplied by the frequency of a photon is equal to the energy of a photon.
The energy of photon is
E=hv=hcλ\mathrm{E}=\mathrm{h} v=\dfrac{\mathrm{hc}}{\lambda}
=(6.6×10−34)(3×108)2×10−9=\dfrac{\left(6.6 \times 10^{-34}\right)\left(3 \times 10^{8}\right)}{2 \times 10^{-9}}
=9.9×10−17 J∼1×10−16 J=9.9\times {{10}^{-17}}~\text{J}\sim1\times {{10}^{-16}}~\text{J}
The approximates energy of a photon given that wavelength of photon is 2 nm and Planck constant h\mathrm{h} is 6.6×10−34 J s6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s} is 1×10−16 J1\times {{10}^{-16}}~\text{J}

So, the Correct option is (C) .

Note:
Photons are known as tiny particles that have no charge and no resting mass. Photons are emitted through charged particles, radioactive decay, etc. Photons always move in the vacuum at the speed of light. Photons can be both destroyed and created. Photons are formed when electromagnetic waves are emitted by the source. When photons strike matter, the energy is either absorbed or transferred to atoms and molecules. Energy and momentum are conserved by the creation and destruction of photons. The radiation law of Planck, a mathematical relationship formulated by German physicist Max Planck in 1900 .