Rutherford, Planck, and Bohr (The Atomic Model)

The modern picture of the atom — a dense, positively charged nucleus orbited by electrons confined to specific energy levels — didn't arrive all at once. It came from three breakthroughs: Max Planck's discovery that energy is quantized, Ernest Rutherford's gold foil experiment revealing the nucleus, and Niels Bohr's model of the hydrogen atom, which combined the two into a working picture of atomic structure and light.

Key Takeaways

• Planck (1900): energy is quantized, emitted/absorbed only in discrete packets (quanta); E = hf.

• Rutherford (1911): the gold foil experiment overturned the plum pudding model, revealing a small, dense, positively charged nucleus surrounded by mostly empty space.

• Bohr (1913): hydrogen's electron occupies quantized circular orbits with angular momentum L = nh/2π; orbit energies follow E = −RH/n²; transitions between orbits absorb/emit energy equal to the level difference.

• Ground state = lowest-energy, most stable; excited state = higher-energy, reached by absorbing a photon or thermal energy.

• Absorption (ground → excited, dark line) and emission (excited → lower level, bright line) together form an element's atomic spectrum — a unique fingerprint used in emission and absorption spectroscopy.

• Hydrogen's spectral lines group into the Lyman (→ n=1, UV), Balmer (→ n=2, visible), and Paschen (→ n=3, infrared) series; the Rydberg formula, 1/λ = RH(1/n₁² − 1/n₂²), calculates the wavelength of any transition.

Planck and the Quantization of Energy

In 1900, Max Planck was studying blackbody radiation — the light emitted by an idealized object that absorbs all radiation striking it — when he arrived at an idea that reshaped physics: energy is not continuous, but quantized. Planck proposed that electromagnetic energy can only be emitted or absorbed in discrete packets called quanta, rather than in a smooth, continuous stream.

The energy of a single quantum is related to the frequency of the radiation by:

E = hf

where E is energy, f is frequency, and h is Planck's constant. This single relationship — that energy comes in discrete, frequency-dependent packets — became the foundation for everything that followed.

Rutherford's Gold Foil Experiment and the Nuclear Model

Before 1911, the leading picture of the atom was the plum pudding model: negatively charged electrons scattered throughout a diffuse, positively charged "pudding." In 1911, Ernest Rutherford overturned this picture with his gold foil experiment, in which alpha particles were fired at a thin sheet of gold foil. Most particles passed straight through, but a small fraction deflected sharply — some almost straight back.

That result was only possible if the atom's positive charge and mass were concentrated in a tiny, dense region rather than spread out. Rutherford's conclusion: the atom has a compact, positively charged nucleus that occupies only a tiny fraction of the atom's total volume, with the rest of the atom being largely empty space where electrons reside.

Bohr's Model of the Hydrogen Atom

Building on Rutherford's nuclear model, Niels Bohr introduced his model of the hydrogen atom in 1913. Bohr proposed that a hydrogen atom's single electron moves in a circular orbit around the nucleus, and that only certain orbits — corresponding to certain fixed energy levels — are allowed.

This was a direct challenge to classical physics, which predicts that an orbiting, charged electron should continuously radiate energy and spiral into the nucleus, collapsing the atom. Bohr's orbits, by contrast, are stable.

Bohr resolved the contradiction by borrowing Planck's idea that energy is quantized. He proposed that an electron's angular momentum is restricted to specific, quantized values:

L = nh/2π

where n is the principal quantum number (a positive integer: 1, 2, 3, ...). Because angular momentum is quantized, only certain orbital radii — and therefore only certain energy levels — are allowed. These allowed orbits are called stationary states, and an electron only gains or loses energy by jumping between them, absorbing or emitting an amount of energy exactly equal to the difference between the two levels.

Bohr expressed the energy of an electron at level n in the hydrogen atom as:

E = −RH/n²

where RH is the Rydberg constant for hydrogen (here, its energy form: ≈2.18×10⁻¹⁸ J, or 13.6 eV). The negative sign reflects that these are bound states: energy is defined as zero when the electron and nucleus are infinitely far apart with no interaction between them. As n increases, the electron sits in a higher, less tightly bound energy level, farther from the nucleus.

Note: "the Rydberg constant" appears in two related but numerically different forms depending on what the formula outputs. The energy form above (≈2.18×10⁻¹⁸ J) differs from the wavenumber form (≈1.097×10⁷ m⁻¹) used in the Rydberg formula later in this article — the two are related by RH(energy) = RH(wavenumber) × hc.

The Bohr model successfully explained the quantized energy levels of hydrogen and its spectral lines — but it has real limitations (it works well only for hydrogen-like, one-electron systems) that a more complete quantum mechanical picture later addressed.

Ground States, Excited States, and Photon Absorption/Emission

Two terms describe an electron's energy state within an atom:

• Ground state: the lowest-energy, most stable configuration. In its ground state, an atom's electrons all occupy the lowest energy levels available to them.

• Excited state: a higher-energy, less stable configuration, reached when an electron absorbs energy — from a photon or from thermal energy — and jumps to a higher level. An excited electron tends to fall back to a lower level, releasing energy in the process.

A transition between energy levels always involves a photon — a particle of light — whose energy exactly matches the difference between the two levels:

• Absorption: an electron in the ground state absorbs a photon of the right energy and jumps to an excited state. This produces a dark line in the absorption spectrum at the wavelength corresponding to that absorbed energy.

• Emission: an excited electron falls to a lower level (often back to the ground state) and emits a photon whose energy equals the gap between the two levels. This produces a bright line in the emission spectrum at that wavelength.

The complete collection of these dark and bright lines forms an element's distinctive atomic spectrum.

Atomic Emission and Absorption Spectroscopy

These absorption and emission processes are the basis of two related analytical techniques:

Atomic emission spectroscopy supplies energy to a sample, exciting its electrons to higher energy levels. As the excited electrons fall back to the ground state, they emit photons. Because the specific wavelengths emitted depend on the exact energy-level structure of the element, the resulting emission spectrum acts as a unique "fingerprint" that identifies which element produced it.

Atomic absorption spectroscopy works in reverse: a light source with a known, continuous spectrum is passed through a sample. Atoms in the sample absorb only the photons whose energy matches the gap between their ground state and an excited state. Analyzing which wavelengths are missing from the transmitted light — the absorption spectrum — reveals which elements are present in the sample.

Both techniques give chemists a way to probe the electronic structure of atoms by studying how they interact with light.

The Hydrogen Spectral Series: Lyman, Balmer, and Paschen

When a hydrogen atom's electron transitions between energy levels, the resulting photons fall into distinct groups called spectral series, depending on which energy level the transition ends on:

The Balmer series is historically significant: because its lines fall in the visible spectrum, they were the first hydrogen spectral lines ever observed and correlated to electronic transitions, by Johann Balmer.

The energy of a transition's emitted or absorbed photon — and therefore its wavelength — can be calculated with the Rydberg formula. The standard form of this equation is:

1/λ = RH(1/n₁² − 1/n₂²)

where λ is the photon's wavelength, RH is the Rydberg constant for hydrogen, n₁ is the principal quantum number of the lower (final) energy level, and n₂ is the principal quantum number of the higher (initial) energy level.

Common MCAT Mistakes

• Mixing up the two forms of the Rydberg constant. The energy form (≈2.18×10⁻¹⁸ J) used in E = −RH/n² is not the same number as the wavenumber form (≈1.097×10⁷ m⁻¹) used in the Rydberg formula — check which formula you're using before plugging in a value.

• Reversing n₁ and n₂ in the Rydberg formula. n₁ is always the lower (final) energy level and n₂ is always the higher (initial) energy level for an emission transition — swapping them flips the sign of the result.

• Confusing absorption and emission lines. Absorption produces dark lines (ground → excited, energy taken in); emission produces bright lines (excited → lower level, energy released) — the two spectra are complementary, not identical.

• Misassigning a transition to the wrong spectral series. The series is defined by which level the transition ends on, not starts on: ending at n = 1 is Lyman (UV), ending at n = 2 is Balmer (visible), ending at n = 3 is Paschen (infrared).

MCAT-Style Concept Check

Question: A hydrogen electron transitions from n = 3 to n = 2, emitting a photon. Which spectral series does this transition belong to, and in what region of the electromagnetic spectrum does the emitted light fall?

• A) Lyman series; ultraviolet

• B) Balmer series; visible

• C) Paschen series; infrared

• D) Balmer series; ultraviolet

Answer: B

Explanation: The transition ends at n = 2, which defines the Balmer series. Using the Rydberg formula with n₁ = 2 and n₂ = 3 and RH ≈ 1.097×10⁷ m⁻¹: 1/λ = 1.097×10⁷ × (1/2² − 1/3²) = 1.097×10⁷ × (0.250 − 0.111) ≈ 1.524×10⁶ m⁻¹, so λ ≈ 656 nm — visible red light, matching the well-known hydrogen-alpha line.

FAQ

What is the Bohr model of the atom?

Bohr's 1913 model proposes that a hydrogen atom's electron moves in fixed, quantized circular orbits around the nucleus, with angular momentum restricted to specific values (L = nh/2π). Electrons only gain or lose energy by jumping between these allowed orbits, absorbing or emitting a photon equal to the energy difference between them.

What is the difference between an atom's ground state and its excited state?

The ground state is an atom's lowest-energy, most stable electron configuration. The excited state is a higher-energy, less stable configuration reached when an electron absorbs a photon or thermal energy and jumps to a higher level; an excited electron tends to fall back down, releasing that energy again.

What is the difference between an emission spectrum and an absorption spectrum?

An emission spectrum shows bright lines at the wavelengths an element's excited electrons emit as they fall to lower energy levels. An absorption spectrum shows dark lines at the wavelengths a sample's electrons absorb as they jump to higher energy levels — the two are complementary patterns for the same element.

What do the Lyman, Balmer, and Paschen series represent?

They're groups of hydrogen spectral lines classified by which energy level a transition ends on: Lyman ends at n = 1 (ultraviolet), Balmer ends at n = 2 (visible light), and Paschen ends at n = 3 (infrared).