JEE Advanced · Physics · 26. Dual Nature

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 ×10⁸ ms^-1. The final momentum of the object is

A $0.3 \times 1 0^{- 17} {kg ms}^{-1}$
B $1.0 \times 1 0^{- 17} {kg ms}^{-1}$
C $3.0 \times 1 0^{- 17} {kg ms}^{-1}$
D $9.0 \times 1 0^{- 17} {kg ms}^{-1}$

Verified Solution

Answer & Solution

Correct Answer

(B) $1.0 \times 1 0^{- 17} {kg ms}^{-1}$

Step-by-step Solution

Detailed explanation

Power = \frac{E}{t} E = Energy ​

∴ E = Power \times time = \frac{hc}{λ}

\frac{hc}{λ} = 30 \times 1 0^{- 3} \times 100 \times 1 0^{- 9}

∴ p = \frac{h}{λ} = \frac{3 \times 1 0^{- 9}}{3 \times 1 0^{8}} = 1 \times 1 0^{-1 7} kg ms

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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	Column - I		Column -II
P.		1.	Diastereomer
Q.		2.	Identical
R.		3.	Enantiomer
S.

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 ×108 ms-1. The final momentum of the object is

Step-by-step Solution

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 ×10⁸ ms^-1. The final momentum of the object is