Chemistry Practice Problems Bohr and Balmer Equations Practice Problems Solution: Before quantum mechanics was developed, Johannes R...

🤓 Based on our data, we think this question is relevant for Professor Holton's class at UCI.

Solution: Before quantum mechanics was developed, Johannes Rydberg developed an equation that predicted the wavelengths (λlambda) in the atomic spectrum of hydrogen: 1/λ = R(1/m2 - 1/n2). In this equation R is a constant and m and n are integers. Use the quantum-mechanical model for the hydrogen atom to derive the Rydberg equation.

Problem

Before quantum mechanics was developed, Johannes Rydberg developed an equation that predicted the wavelengths (λ) in the atomic spectrum of hydrogen: 1/λ = R(1/m2 - 1/n2). In this equation R is a constant and m and n are integers. Use the quantum-mechanical model for the hydrogen atom to derive the Rydberg equation.

Solution
  • For an H atom, the energy of an electron in level n is represented as:

  • An electron jumping from higher energy level f to lower energy level i, the energy released by atom will appear as:

  • Use the equation of En to find the ΔE.

Solution BlurView Complete Written Solution