Bohr's Atomic Model and Quantum Numbers Analysis

Bohr's Postulates of Atomic Structure

Bohr's Postulates: Electrons in an atom revolve around the nucleus in certain fixed circular paths called orbits. Each orbit has a fixed amount of energy, so these are also called energy levels. These levels are denoted by 1, 2, 3, 4 or K, L, M, N.

As long as an electron revolves around the nucleus in a fixed orbit, it does not emit or absorb energy; therefore, these are also called stationary orbits. The angular momentum of a revolving electron is quantized and is an integral multiple of h/2π:

mvr = nh/2π

Where:

• m = mass of electron
• v = velocity
• r = radius
• h = Planck's constant

Energy is emitted or absorbed when an electron jumps from one orbit to another. The energy difference between two orbits is ΔE = E₂ - E₁ = hν, where E₂ is the energy of the higher orbit and E₁ is the energy of the lower orbit.

Hydrogen Spectrum and Bohr's Explanation

When an electric discharge is passed through gaseous hydrogen, the electrons in the atoms absorb energy and jump into higher energy orbits. In higher orbits, they have more energy and less stability. Then, the excited electrons come back to lower orbits in one or multiple steps. Energy is released during this process and appears in the form of spectral lines.

• When an electron jumps from any higher orbit to n=1, it produces spectral lines in the UV region named the Lyman series.
• Jumping to n=2 produces lines in the visible region named the Balmer series.
• Jumping to n=3, 4, or 5 produces spectral lines in the near-IR, IR, and far-IR regions; these are named the Paschen, Brackett, and Pfund series respectively.

From the Rydberg equation, the wave number (1/λ) is calculated as: R_H [1/n₁² - 1/n₂²].

Quantum Numbers and Atomic Orbitals

The quantum numbers n, l, and m are arrived at by solving the Schrödinger wave equation. They explain the position of the electron, the size of the orbit, and the shape and orientation of orbitals.

Principal Quantum Number (n)

Proposed by Bohr and denoted by n, the values of n are 1, 2, 3, 4 or K, L, M, N. Its significance is that it denotes the size and energy of the orbit. The maximum number of electrons in the nth orbit is 2n².

Azimuthal Quantum Number (l)

Proposed by Sommerfeld and denoted by l, the values of l range from 0 to n-1.