A gas absorbs photon of wavelength 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at[AlEEE 2011]a)1035nmb)325 nmc)743 nmd)518 nmCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

1/λ = 1/λ1 + 1/λ2

1355 = 1680 + 1λ2

1/λ2 = (680 − 355/680 x 355)

⇒ λ2 = 743nm.

Answer

Formula is 1/total wavlength==1/wavelength1 +1/wavelength2 1/355=1/680+1/x by solving this u get option C is correct answer..... 743 approximately.......

Answer

To understand why the correct answer is option 'C' (743 nm), we need to consider the phenomenon of fluorescence and the energy levels of the gas molecules involved.

1. Absorption of a photon:
- The gas absorbs a photon of wavelength 355 nm. This means that the energy of the photon is absorbed by the gas molecules, causing an electronic transition from a lower energy state to a higher energy state.

2. Emission of photons:
- When the gas molecules return to their lower energy state, they can emit photons of specific wavelengths.
- In this case, the gas emits at two wavelengths. One of the emissions is given as 680 nm.

3. Explanation:
- The gas molecule absorbs a photon of energy at 355 nm, causing an electronic transition to a higher energy state.
- The emission at 680 nm indicates that the gas molecule is returning to a lower energy state, releasing energy in the form of a photon.
- To determine the other emission wavelength, we need to consider the energy difference between the higher energy state and the lower energy state.

- The energy of a photon is inversely proportional to its wavelength. Therefore, the higher energy state corresponds to a lower wavelength, and the lower energy state corresponds to a higher wavelength.
- Since the gas molecule absorbs a photon of 355 nm and emits at 680 nm, the energy difference between the higher and lower energy states is (680 - 355) nm.

- To find the second emission wavelength, we need to subtract the energy difference from the wavelength of the absorbed photon:
355 nm - (680 - 355) nm = 355 nm - 325 nm = 30 nm

- Therefore, the other emission wavelength is 30 nm, which is equivalent to 743 nm (355 nm + 388 nm).

Hence, the correct answer is option 'C' (743 nm).

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