JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Modern Physics

For hydrogen atom,

λ_{1}

and

λ_{2}

are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of

λ_{1}

and

λ_{2}

\frac{x}{32}

. The value of

x

____

Answer: 27

Solution

From the level diagram, transition 1 is the jump from

n = 3

n = 1

and transition 2 is the jump from

n = 2

n = 1

. The Rydberg relation gives

\frac{1}{λ _{1}} = R (1 - \frac{1}{9}) = \frac{8 R}{9}

and

\frac{1}{λ _{2}} = R (1 - \frac{1}{4}) = \frac{3 R}{4}

. Dividing,

\frac{λ _{1}}{λ _{2}} = \frac{1/ λ _{2}}{1/ λ _{1}} = \frac{3 R /4}{8 R /9} = \frac{3}{4} \times \frac{9}{8} = \frac{27}{32}

, so

x = 27

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Integer answer

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