Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Electromagnetic waves carry energy but not momentum.
Reason (R): Mass of a photon is zero. In the light of the above statements.
choose the most appropriate answer from the options given below:
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Electromagnetic waves carry energy but not momentum.
Reason (R): Mass of a photon is zero. In the light of the above statements.
choose the most appropriate answer from the options given below:
Show Hint
- Both (A) and (R) are true and (R) is the correct explanation of (A)
- (A) is false but (R) is true
- Both (A) and (R) are true but (R) is not the correct explanation of (A)
- (A) is true but (R) is false
The Correct Option is C
Approach Solution - 1
To evaluate the given statements and determine the correct option, we need to analyze both the Assertion (A) and the Reason (R).
Assertion (A): Electromagnetic waves carry energy but not momentum.
Electromagnetic waves, which include light, do indeed carry energy. However, contrary to the assertion, they also carry momentum. The momentum (\( p \)) of a photon is related to its energy (\( E \)) by the equation:
\( p = \frac{E}{c} \)
where \( c \) is the speed of light. Hence, the assertion is false.
Reason (R): Mass of a photon is zero.
This statement is true. Photons are massless particles and this fact is significant in relativity and quantum mechanics.
Analysis:
While Reason (R) is true, it does not correctly explain Assertion (A) because Assertion (A) itself is incorrect. The correct understanding is that electromagnetic waves carry both energy and momentum. Thus, the appropriate conclusion is:
The correct answer is: both (A) and (R) are true, but (R) is not the correct explanation of (A).
Approach Solution -2
Assertion (A): Electromagnetic waves carry energy but not momentum.
Reason (R): Mass of a photon is zero.
Step 2: Analyze Assertion (A).
Electromagnetic waves are composed of oscillating electric and magnetic fields that propagate through space. These waves carry both energy and momentum. The energy density of an electromagnetic wave is given by:
\[ u = \frac{1}{2} \varepsilon_0 E^2 + \frac{1}{2\mu_0} B^2, \] and the momentum associated with the wave is given by the Poynting vector divided by the speed of light \( c \).
Hence, electromagnetic waves indeed carry momentum in addition to energy. Therefore, the assertion (A) is **false** because electromagnetic waves do carry momentum.
Step 3: Analyze Reason (R).
The mass of a photon is indeed zero, but a photon still carries energy \( E = h\nu \) and momentum \( p = \frac{E}{c} \). The absence of rest mass does not imply the absence of momentum.
Thus, the reason (R) is true, but it does not correctly explain the incorrect assertion (A).
Step 4: Conclusion.
Both (A) and (R) are true statements, but (R) does not provide the correct explanation for (A). The correct reasoning should be that electromagnetic waves carry both energy and momentum, despite having zero rest mass for photons.
Final Answer:
Both (A) and (R) are true but (R) is not the correct explanation of (A).
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