A light of wavelength N is absorted. It emits two radiations of wavelength N1 and N2 then, 1. N= N1+N2 2. N= N1-N23. N= N1N2/(N1+N2) 4. N=(N1+N2)/(N1+N2)

To tackle the question about the relationship between the wavelengths of absorbed and emitted light, we need to delve into some fundamental concepts of light absorption and emission. When a substance absorbs light of a certain wavelength (let's call it N), it can re-emit energy in the form of light at different wavelengths (N1 and N2). The options you've provided suggest different mathematical relationships between these wavelengths. Let's analyze them one by one.

Understanding Light Absorption and Emission

When a photon of light is absorbed by an atom or molecule, it can excite electrons to a higher energy level. When these electrons return to their original state, they release energy, which can be emitted as light. The wavelengths of the emitted light can vary based on the energy transitions that occur within the atom or molecule.

Analyzing the Options

• Option 1: N = N1 + N2

This suggests that the absorbed wavelength is equal to the sum of the emitted wavelengths. This is not typically how energy conservation works in quantum mechanics, as the energy absorbed does not simply add up to the emitted wavelengths.

• Option 2: N = N1 - N2

This implies that the absorbed wavelength is the difference between the two emitted wavelengths. While this could theoretically happen in certain scenarios, it does not represent a general rule for light absorption and emission.

• Option 3: N = (N1 * N2) / (N1 + N2)

This formula resembles the concept of harmonic mean, which is used in various physical contexts. However, it does not directly apply to the relationship between absorbed and emitted wavelengths in a straightforward manner.

• Option 4: N = (N1 + N2) / (N1 + N2)

This simplifies to N = 1, which is nonsensical in the context of wavelengths. It does not provide any meaningful relationship between the absorbed and emitted wavelengths.

Conclusion on the Relationships

None of the options provided accurately describe the relationship between the absorbed wavelength (N) and the emitted wavelengths (N1 and N2) in a general sense. In quantum mechanics, the energy of the absorbed photon corresponds to the energy difference between the excited state and the ground state of the atom or molecule. The emitted wavelengths depend on the specific energy transitions that occur during the emission process.

In summary, while the absorption and emission of light involve complex interactions, the relationships given in the options do not hold true in a general context. If you're looking for a specific relationship, it would be more beneficial to study the principles of energy conservation and quantum transitions in detail.