Concepts Of Physics MCQ Edition [Volume 2]PhysicsBohr's Model and Physics of the Atom
A collection of hydrogen atoms is prepared in the n = 4 state. Identify the wavelengths of the radiation emitted as the atoms make transitions and return to the n = 2 state.
Options
- A487 nm , 654 nm , 1910 nm
- B97 nm , 103 nm , 122 nm
- C434 nm , 1281 nm , 4050 nm
- D487 nm , 654 nm , 122 nm
Correct answer
A. 487 nm , 654 nm , 1910 nm
Step-by-step solution
The possible transitions for a hydrogen atom returning from the n=4 state to the n=2 state are: n=4 n=2 n=4 n=3 n=3 n=2 Using the Rydberg formula for the wavelength of emitted radiation: 1 = R ( 1 n_f^2 - 1 n_i^2 ) where R 1.097 10^7 m ⁻¹ . For the n=4 n=2 transition: 1 ₁ = R ( 1 2^2 - 1 4^2 ) = R ( 1 4 - 1 16 ) = 3R 16 ₁ = 16 3R 486 nm For the n=3 n=2 transition: 1 ₂ = R ( 1 2^2 - 1 3^2 ) = R ( 1 4 - 1 9 ) = 5R 36 ₂ = 36 5R 656 nm For the n=4 n=3 transition: 1 ₃ = R ( 1 3^2 - 1 4^2 ) = R ( 1 9 - 1 16 ) = 7R 144 ₃