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Physics - Modern Physics Question with Solution | TestHub

PhysicsModern PhysicsAtomic structureHard2 minQB

PhysicsHardnumerical

As per given figure $A, B$ and $C$ are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavelengths $(i . e . \frac{λ _{1}}{λ _{2}})$ is $\frac{7}{4 n}$ , then the value of $n$ will be

Answer:

5.00

Solution:

For $λ_{1}$
$\frac{1}{λ _{1}} = R Z^{2} (\frac{1}{2 ^{2}} - \frac{1}{3 ^{2}}) = R (\frac{5}{36}) ... (i)$
For $λ_{2}$ ,
$\frac{1}{λ _{2}} = R Z^{2} (\frac{1}{3 ^{2}} - \frac{1}{4 ^{2}}) = R (\frac{7}{144}) ... (ii)$
Dividing (ii) by (i)
$\frac{λ _{1}}{λ _{2}} = \frac{\frac{7}{144}}{\frac{5}{36}} = \frac{7}{20}$
So,
$\frac{7}{4 n} = \frac{7}{20} \Rightarrow n = 5$

Stream:JEESubject:PhysicsTopic:Modern PhysicsSubtopic:Atomic structure

⏱ 2mℹ️ Source: QB

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