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 Li ⁺⁺ .
Options
- A273 nm
- B10 nm
- C91 nm
- D30 nm
Correct answer
B. 10 nm
Step-by-step solution
The smallest wavelength of emitted radiation corresponds to the maximum energy transition, which occurs when an electron transitions from n = to n = 1 . Using the Rydberg formula for hydrogen-like species: 1 = R Z^2 ( 1 n₁^2 - 1 n₂^2 ) For Li ⁺⁺ , the atomic number Z = 3 . Substituting n₁ = 1 and n₂ = : 1 = R (3)^2 ( 1 1^2 - 0 ) 1 = 9R = 1 9R Since 1 R 91.2 nm : = 91.2 nm 9 10.13 nm The closest value among the given options is 10 nm .