Concepts Of Physics MCQ Edition [Volume 2]PhysicsBohr's Model and Physics of the Atom
Determine the smallest wavelength of radiation that can be emitted by hydrogen.
Options
- A365 nm
- B91 nm
- C122 nm
- D820 nm
Correct answer
B. 91 nm
Step-by-step solution
The smallest wavelength of radiation emitted by a hydrogen atom corresponds to the maximum energy transition. This maximum energy transition occurs when an electron falls from n = to n = 1 (the series limit of the Lyman series). Using the Rydberg formula: 1 = R ( 1 n₁^2 - 1 n₂^2 ) Substituting n₁ = 1 and n₂ = : 1 = R ( 1 1^2 - 1 ^2 ) = R = 1 R Substituting the value of the Rydberg constant R = 1.097 10^7 m ⁻¹ : = 1 1.097 10^7 m 91.1 10⁻⁹ m = 91.1 nm Thus, the smallest wavelength is approximately 91 nm .