Given below are two statements Statement\(-I :\) Two photons having equal linear momenta have equal wavelengths. Statement\(-II :\) If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease. In the light of the above statements, choose the correct answer from the options given below.

A Both Statement \(I\) and Statement \(II\) are true
B Statement \(I\) is false but Statement \(II\) is true
C Both Statement \(I\) and Statement \(II\) are false
D Statement \(I\) is true but Statement \(II\) is false

Verified Solution

Answer & Solution

Correct Answer

(D) Statement \(I\) is true but Statement \(II\) is false

Step-by-step Solution

Detailed explanation

If linear momentum are equal then wavelength also equal \(p=\frac{h}{\lambda}, E=\frac{h c}{\lambda}\) On decreasing wavelength, momentum and energy of photon increases.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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