Bohr model of the hydrogen atom
Explains Bohr's postulates for atomic structure, leading to quantized energy levels and stable orbits.
What is Bohr model of the hydrogen atom?
Fundamental assumptions made by Niels Bohr to explain the stability and spectrum of the hydrogen atom, including stationary orbits, quantized angular momentum, and energy transitions.
Key formula / rule: Quantization of Angular Momentum
Key points
- State Bohr's postulates for the hydrogen atom.
- Derive expressions for the radius, velocity, and energy of an electron in a Bohr orbit.
- Calculate the energy of different energy levels and transition energies for hydrogen and hydrogen-like atoms.
- Explain the origin of spectral lines in the hydrogen spectrum.
Common exam trap
Confusing Bohr's postulates with Rutherford's model.
Definitions
- Term
Bohr's Postulates
- Meaning
Fundamental assumptions made by Niels Bohr to explain the stability and spectrum of the hydrogen atom, including stationary orbits, quantized angular momentum, and energy transitions.
- Term
Quantization
- Meaning
The concept that certain physical quantities, such as energy or angular momentum, can only take on discrete, specific values rather than a continuous range.
- Term
Stationary Orbits
- Meaning
Specific, stable electron orbits in which an electron can revolve around the nucleus without radiating energy, as proposed by Bohr.
- Term
Ionization Energy
- Meaning
The minimum energy required to remove an electron completely from an atom in its ground state (n=1 to n=∞).
- Term
Excitation Energy
- Meaning
The energy required to move an electron from its ground state to a higher energy level (e.g., n=1 to n=2).
Learning objectives
State Bohr's postulates for the hydrogen atom.
Derive expressions for the radius, velocity, and energy of an electron in a Bohr orbit.
Calculate the energy of different energy levels and transition energies for hydrogen and hydrogen-like atoms.
Explain the origin of spectral lines in the hydrogen spectrum.
Identify the successes and limitations of the Bohr model.
Formulae
- Name
Quantization of Angular Momentum
- Note
Where n is the principal quantum number (n=1, 2, 3...), m is electron mass, v is electron velocity, r is orbit radius, h is Planck's constant.
- Expression
L = mvr = n(h/2π)
- Name
Radius of n-th Bohr Orbit
- Note
a₀ is the Bohr radius (0.529 Å or 5.29 x 10⁻¹¹ m). Z is the atomic number.
- Expression
rn = (n²h²ε₀) / (πmZ e²) = a₀ (n²/Z)
- Name
Velocity of electron in n-th Bohr Orbit
- Note
Related to speed of light c and fine structure constant α (vn = αc Z/n).
- Expression
vn = (Z e²) / (2ε₀ n h)
- Name
Energy of electron in n-th Bohr Orbit
- Note
Negative sign indicates a bound state. En is inversely proportional to n².
- Expression
En = -(mZ²e⁴) / (8ε₀²h²n²) = -13.6 (Z²/n²) eV
- Name
Energy of Emitted/Absorbed Photon
- Note
For emission, Efinal < Einitial. For absorption, Efinal > Einitial.
- Expression
ΔE = Efinal - Einitial = hν = hc/λ
- Name
Rydberg Formula for Spectral Lines
- Note
R is the Rydberg constant (1.097 x 10⁷ m⁻¹). n₁ is the lower energy level, n₂ is the higher energy level (n₂ > n₁).
- Expression
1/λ = RZ²(1/n₁² - 1/n₂²)
Prerequisites
Basic understanding of atomic structure (Rutherford's model).
Concepts of centripetal force and electrostatic force.
Knowledge of Planck's constant and photon energy (E=hν).
Basic algebra and unit conversions.
Common mistakes
Confusing Bohr's postulates with Rutherford's model.
Incorrectly applying Bohr's model to multi-electron atoms.
Forgetting the negative sign in the energy expression (indicating bound state).
Not understanding that energy is absorbed for excitation and emitted for de-excitation.
Incorrectly using Z for hydrogen (Z=1) in general formulas.
Keywords
Bohr model
Hydrogen atom
Atomic structure
Quantization
Energy levels
Spectral series
Rydberg formula
Angular momentum
Stationary orbits
NEET Physics
Practice preview
According to the Bohr model, the angular momentum of an electron in any particular orbit is quantized. Which of the following expressions represents the quantized angular momentum?…
easy
When an electron in a hydrogen atom transitions from a higher energy level to a lower energy level, it emits energy in the form of a photon. What is the relationship between the energy difference (ΔE) and the frequency (…
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The radius of the Bohr orbit for a hydrogen atom is given by the formula r = n²a₀, where a₀ is the Bohr radius. If an electron is in the third orbit (n=3), what is the ratio of its orbit's radius to the radius of the fir…
medium