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. A radiation detector is positioned near the gas to detect radiation propagating perpendicular to the incident beam. Find th
Options
- A121 nm , 654 nm
- B103 nm , 121 nm , 654 nm
- C100 nm , 103 nm , 121 nm
- D103 nm , 560 nm , 654 nm
Correct answer
B. 103 nm , 121 nm , 654 nm
Step-by-step solution
The energy of the incident photon is given by: E = hc = 1242 eV nm 100 nm = 12.42 eV The energy required to excite a hydrogen atom from the ground state ( n=1 ) to higher energy states is: E_ 1 2 = 13.6 (1 - 1 2^2 ) = 10.2 eV E_ 1 3 = 13.6 (1 - 1 3^2 ) = 12.09 eV E_ 1 4 = 13.6 (1 - 1 4^2 ) = 12.75 eV Since the incident photon energy ( 12.42 eV ) is greater than 12.09 eV but less than 12.75 eV , the hydrogen atoms can be excited to the n=2 and n=3 states. The remaining energy is carried by photons moving in the forw