Assertion (A) : The quantum of energy of an elastic wave is called phonon.
Reason (R) : The energy of each phonon is $\epsilon = h\nu$.
In the light of the above statements, choose the most appropriate answer from the options given below :
Assertion (A) Analysis: Phonon Definition
The assertion states that a phonon is the quantum of energy of an elastic wave. In physics, particularly solid-state physics, phonons represent quantized modes of vibration occurring in a rigid crystal lattice. These quantized vibrations are analogous to photons, which are quanta of the electromagnetic field. Therefore, a phonon is indeed considered the quantum of vibrational energy in a crystal, often associated with elastic waves within the material.
Conclusion: Statement (A) is correct.
Reason (R) Analysis: Phonon Energy Formula
The reason provides the formula for the energy of a phonon as $\epsilon = h\nu$. Here, $\epsilon$ represents the energy of the phonon, $h$ is Planck's constant, and $\nu$ is the frequency of the lattice vibration.
This formula correctly describes the energy of a phonon, similar to how the energy of a photon is given by $E = h\nu$. The energy is directly proportional to the frequency of the vibration.
Conclusion: Statement (R) is correct.
Relationship Between Assertion (A) and Reason (R)
Statement (A) defines a phonon as the quantum of energy for elastic waves (lattice vibrations). Statement (R) provides the exact mathematical expression for this quantum of energy ($\epsilon = h\nu$). The formula in (R) quantifies the concept introduced in (A), explaining *how* the energy is quantized in terms of frequency.
Therefore, the energy formula ($\epsilon = h\nu$) is the correct explanation for why a phonon is considered the quantum of energy of an elastic wave.
Conclusion: Reason (R) is the correct explanation of Assertion (A).
Final Answer Determination
Based on the analysis:
- Assertion (A) is correct.
- Reason (R) is correct.
- Reason (R) correctly explains Assertion (A).
The most appropriate option is that both (A) and (R) are correct, and (R) is the correct explanation of (A).
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Important Questions from Mixed Topic (CUET PG)
- Kalpsutra, the illustrated canonical text is from:-
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- Mohandas Karamchand Gandhi launched quit India movement after the failure of:-
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- Who among the following was not a member of the constituent assembly:-
