Bohr's Model For The Hydrogen Atom

Bohr's Postulates

Niels Bohr (1913) used Planck's concept of quantization to improve Rutherford's model. His theory rests on a few core rules about how electrons behave around the nucleus.

First, electrons move in fixed circular paths called orbits (or stationary states). An electron in an allowed orbit does not radiate energy, keeping the atom stable.

Worked Example: Hydrogen-like Ions

Problem. Calculate the energy associated with the first orbit of $\text{He}^+$. What is the radius of this orbit?

(This is based on Problem 2.11)

Given:

• Ion: $\text{He}^+$ (Helium has an atomic number $Z = 2$)
• Orbit: First orbit ($n = 1$)

Worked Example: Frequencies of Transitions

Problem. What are the frequency and wavelength of a photon emitted during a transition from the $n = 5$ state to the $n = 2$ state in the hydrogen atom?

(This is based on Problem 2.10)

Given:

• Initial state: $n_i = 5$
• Final state: $n_f = 2$

Limitations of Bohr's Model

While Bohr's model was a massive leap forward and perfectly explained the hydrogen line spectrum, it was too simplistic to account for the complexity of the quantum world.

Eventually, scientists realized a completely new framework (Quantum Mechanics) was required.