Concepts Of Physics MCQ Edition [Volume 2]PhysicsBohr's Model and Physics of the Atom
A parallel beam of light of wavelength 100 nm passes through a sample of atomic hydrogen gas in the ground state. Assume that when a photon supplies a portion of its energy to a hydrogen atom, the remaining energy emerges as another photon travelling in the same direction as the incident photon. Disregarding the light emitted by the excited hydrogen atoms in the direction of the incident beam, what wavelengths can be
Options
- A100 nm , 560 nm , 3880 nm
- B560 nm , 3880 nm
- C100 nm , 121 nm , 103 nm
- D100 nm , 654 nm , 3880 nm
Correct answer
A. 100 nm , 560 nm , 3880 nm
Step-by-step solution
Energy of the incident photon is given by: E = hc = 1240 eV nm 100 nm = 12.4 eV The energy levels of a hydrogen atom are E_n = - 13.6 n^2 eV . The energy required to excite a hydrogen atom from the ground state ( n=1 ) to higher states is: For n=2 : E₁₂ = 13.6 (1 - 1 4 ) = 10.2 eV For n=3 : E₁₃ = 13.6 (1 - 1 9 ) 12.08 eV For n=4 : E₁₄ = 13.6 (1 - 1 16 ) = 12.75 eV Since the incident photon energy ( 12.4 eV ) is less than 12.75 eV , it can only excite the atom to n=2 or n=3 . When the atom is excited to n=2 , the re