Bohr Model of the Hydrogen Atom: Full Explanation
1. Introduction
The Bohr model of the hydrogen atom, proposed by Niels Bohr in 1913, was a major advancement
in atomic theory. It successfully explained the quantization of electron energy levels and the
emission spectra of hydrogen. Bohr combined classical physics with new quantum ideas, laying the
foundation for modern quantum mechanics.
2. Postulates of Bohr's Model
(a) Electrons move in fixed orbits (energy levels)
- Electrons revolve around the nucleus in discrete circular orbits without radiating energy.
- These orbits are called stationary states or energy levels and are represented by principal quantum
numbers (n = 1, 2, 3, ...).
(b) Quantization of angular momentum
- The angular momentum (L) of an electron in an allowed orbit is quantized:
L = m v r = n h / 2pi
where:
- m = mass of the electron
- v = velocity of the electron
- r = radius of the orbit
- h = Planck's constant (6.626 × 10^-34 J·s)
- n = Principal quantum number (1, 2, 3, ...)
(c) Energy is emitted or absorbed in quantized amounts
- When an electron jumps from a higher energy level (E2) to a lower energy level (E1), it emits
energy as a photon.
- The energy difference is given by Planck's equation:
E=hf
where:
- f = frequency of emitted or absorbed radiation.
3. Energy Levels in Hydrogen Atom
The energy of an electron in the nth orbit of hydrogen is given by:
1. Introduction
The Bohr model of the hydrogen atom, proposed by Niels Bohr in 1913, was a major advancement
in atomic theory. It successfully explained the quantization of electron energy levels and the
emission spectra of hydrogen. Bohr combined classical physics with new quantum ideas, laying the
foundation for modern quantum mechanics.
2. Postulates of Bohr's Model
(a) Electrons move in fixed orbits (energy levels)
- Electrons revolve around the nucleus in discrete circular orbits without radiating energy.
- These orbits are called stationary states or energy levels and are represented by principal quantum
numbers (n = 1, 2, 3, ...).
(b) Quantization of angular momentum
- The angular momentum (L) of an electron in an allowed orbit is quantized:
L = m v r = n h / 2pi
where:
- m = mass of the electron
- v = velocity of the electron
- r = radius of the orbit
- h = Planck's constant (6.626 × 10^-34 J·s)
- n = Principal quantum number (1, 2, 3, ...)
(c) Energy is emitted or absorbed in quantized amounts
- When an electron jumps from a higher energy level (E2) to a lower energy level (E1), it emits
energy as a photon.
- The energy difference is given by Planck's equation:
E=hf
where:
- f = frequency of emitted or absorbed radiation.
3. Energy Levels in Hydrogen Atom
The energy of an electron in the nth orbit of hydrogen is given by:
