Concepts Of Physics MCQ Edition [Volume 2]PhysicsBohr's Model and Physics of the Atom
A hot gas emits radiation exclusively at wavelengths of 46.0 nm , 82.8 nm , and 103.5 nm . Assume the atoms possess only two excited states, and the energy difference between consecutive levels decreases with increasing energy. If the energy of the highest state is taken as zero, determine the energies of the ground state and the first excited state.
Options
- A-15 eV and -12 eV
- B-27 eV and -12 eV
- C-27 eV and -15 eV
- D-12 eV and -27 eV
Correct answer
B. -27 eV and -12 eV
Step-by-step solution
The energies of the emitted photons are calculated using E = hc , taking hc = 1242 eV nm . E_a = 1242 46.0 = 27 eV E_b = 1242 82.8 = 15 eV E_c = 1242 103.5 = 12 eV The gas has three energy levels: ground state E₁ , first excited state E₂ , and second excited state E₃ . The highest energy transition corresponds to E₃ - E₁ = 27 eV . The other two transitions are E₂ - E₁ and E₃ - E₂ , which must be 15 eV and 12 eV . It is given that the energy difference between consecutive levels decreases with increasing energy, whi