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A gas absorbs a photon of 355 nm and emits two wavelengths. If one of the emission is at 680 nm, the other is at:
(A) 518 nm
(B) 1035 nm
(C) 325 nm
(D) 743 nm

Answer
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Hint: A photon is the smallest discrete amount of electromagnetic radiation. It is a basic unit of all light. Here, we have to find emission of other wavelengths. And wavelength is related to energy by equationE=hcλ,where h is Planck’s constant, c is velocity of light , λ is wavelength, E is energy.


Complete step by step solution:
- From the law of conservation of energy, that is energy of absorbed photons must be equal to combined energy of two emitted photons.
ET=E1+E2
Consider this equation as equation (1),
Where, ET=total energy of photon, E1=energy of first emitted photon, E2=energy of second emitted photon.
- Now, energy E and wavelength of a photon are related by the equation: E=hcλ
Consider this equation as equation (2),
Where h is Planck’s constant, c is velocity of light.
-Now by inserting values from equation (2) to equation (1) we get,
hcλT=hcλ1+hcλ2
Where, λT=total wavelength, λ1=first wavelength, λ2=second wavelength
In this equation, the values of hc cancels out and we get the formula,
1λT=1λ1+1λ2
Consider this equation as equation (3),
Now by substituting the given values in equation (3) we get,
1355=1680+1λ2
1λ2=135516801λ2=680355355×680λ2=743nm

So, the correct answer is “Option D”.

Additional Information:
- It is found that Photons are always in motion and in vacuum, these travel at a constant speed of 2.998×108m/s. This is commonly called the speed of light, which is denoted by the letter c.
- Energy of a photon is also found to be dependent on its frequency (that is how fast the electric and magnetic field wiggle), the higher the frequency, the more energy the photon has.
- The law of conservation of energy can be seen in everyday examples like-this energy can be used to rotate the turbine of a generator to produce electricity. And in this process the potential energy of water can be tuned into kinetic energy which can on further process will become electric energy.

Note: -One should not get confused in the relation of wavelength and frequency with energy. Wavelength is denoted by symbol λand frequency by symbol ν , and as wavelength increases energy decreases and as frequency increases energy also increases.
- We should not forget to write the unit after solving any question. Here, we can see that the unit of wavelength is nm.


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