The wavelength of radiation emitted is λ₀ when an electron jumps from the second excited state to the first excited state of a hydrogen atom. If the electron jumps from the third excited state to the second orbit, the emitted wavelength is (20λ₀/x). The value of x is:
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
JEE Mains 25 January 2023 Morning Shift

Question

The wavelength of radiation emitted is λ₀ when an electron jumps from the second excited state to the first excited state of a hydrogen atom. If the electron jumps from the third excited state to the second orbit, the emitted wavelength is (20λ₀/x). The value of x is:

Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model

JEE Mains 25 January 2023 Morning Shift

G1 Physics · Accepted Answer

Second excited to first excited means 3→2: E₃₂ = 13.6(1/2² - 1/3²). Third excited to second orbit means 4→2: E₄₂ = 13.6(1/2² - 1/4²). Since wavelength is inversely proportional to transition energy, (20/x) = E₃₂/E₄₂ = 20/27. Hence x = 27.