Q52 / 57 · JEE Advanced 2021 (Paper 1) · Physics

Which of the following statement(s) is (are) correct about the spectrum of hydrogen atom?

  • Correct answer
    A
    The ratio of the longest wavelength to the shortest wavelength in Balmer series is 95.
  • B
    There is an overlap between the wavelength ranges of Balmer and Paschen series.
  • C
    The wavelengths of Lyman series are given by 1+1m2λ0, where λ0 is the shortest wavelength of Lyman series and m is an integer.
  • Correct answer
    D
    The wavelength ranges of Lyman and Balmer series do not overlap.

Solution

Figure

For Balmer Series:

Shortest wavelength, Eo4=hcλs

Longest wavelength, Eo4−E09=hcλl=5Eo36

∴ λlλs=95

Range of energy level in Balmer series,

5E036, E04

Range of energy level in Paschen series,

7E0144, E09

Hence, no overlap.

For Lyman series:

For shortest wavelength,

E0=hcλ0

For general wavelength,

E0-E0n2=hcλ

⇒11−1n2=λλ0

∴ λ=n2n2−1λ0

or λ=1+1n2−1λ0=1+1m2λ0

as m should be an integer.

Range of energy level in Lyman series, 3E04, E0

⇒ Lyman and Balmer series wavelengths do not overlap.

Hence, the correct answer is options: 'A', 'D'.

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