TS EAMCET · Chemistry · Structure of Atom

The velocities of two particles $A$ and $B$ are 0.05 and $0.02 \mathrm{~ms}^{-1}$ respectively. The mass of $B$ is five times the mass of $A$. The ratio of their de-Broglie's wavelength is

A $2: 1$
B $1: 4$
C $1: 1$
D $4: 1$

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Answer & Solution

Correct Answer

(A) $2: 1$

Step-by-step Solution

Detailed explanation

Given, velocity of particle $A=0.05 \mathrm{~ms}^{-1}$ Velocity of particle $B=0.02 \mathrm{~ms}^{-1}$ Let the mass of particle $A=x$ $\therefore$ The mass of particle $B=5 x$ de-Broglie's equation is \[ \lambda=\frac{h}{m v} \] For particle $A$…

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.

Same subject

Match the following.

	Column-1 Reaction		Column-2 Main product
A	${SO}_{3} \overset{heavy water}{⟶}$	I	$C_{2} D_{2}$
B	${CaC}_{2} \overset{heavy water (excess)}{⟶}$	II	${CD}_{4}$
C	${Al}_{4} C_{3} \overset{heavy water (large excess)}{⟶}$	III	$D_{2} {SO}_{3}$
		IV	$C_{2} D_{4}$
		V	$D_{2} {SO}_{4}$

The correct match is

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The velocities of two particles \(A\) and \(B\) are 0.05 and \(0.02 \mathrm{~ms}^{-1}\) respectively. The mass of \(B\) is five times the mass of \(A\). The ratio of their de-Broglie's wavelength is

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