Development of the Atomic Model (Thomson → Rutherford → Bohr)原子模型的发展（汤姆孙 → 卢瑟福 → 玻尔）

This time, follow the data

Lesson 1.3.7 told the story of atomic models from Dalton to the electron cloud: each new model appeared because the old one couldn’t explain some experiment. This lesson retraces that history through the data: what each experiment actually measured, and how those numbers led to new conclusions.

Thomson: cathode rays and the electron (1897)

Put a few thousand volts across the two ends of an evacuated glass tube, and a beam of invisible rays streams from the negative electrode (the cathode), making the glass glow where it hits. These are cathode rays. A charged particle that flies through an electric field (for example, between two charged metal plates) or a magnetic field feels a force, so its path bends; this is called deflection. In an electric field, negative particles bend toward the positive plate and positive particles toward the negative plate. J. J. Thomson found that:

• The beam bends toward a positive plate in an electric field and is also deflected by a magnet, so it’s a stream of negatively charged particles.
• From how much the beam bends in electric and magnetic fields, he could calculate the particles’ charge-to-mass ratio比荷 (charge is measured in coulombs, C, so the ratio is in coulombs per kilogram, C/kg):

• Changing the cathode metal or the gas in the tube didn’t change the ratio at all.

So these negative particles exist in every kind of atom: they’re electrons. Their charge-to-mass ratio is about 1840 times that of a hydrogen ion ($9.58 \times 10^{7}$ C/kg), so they must be either far lighter than a hydrogen atom or far more highly charged. Thomson argued for the first, and built his “plum pudding” model on it.

A ratio alone, though, doesn’t tell you the charge or the mass separately. That took another experiment.

Millikan: the oil-drop experiment (1909)

Robert Millikan sprayed tiny oil droplets between two horizontal charged metal plates. The drops picked up electric charge as they were sprayed. By adjusting the voltage so that the electric force balanced gravity and a drop hung still, he could calculate the charge on that drop. After measuring many drops, he found that every charge was a whole-number multiple of one smallest value: charge comes in fixed packets. That smallest charge, the size of the charge on one electron, is the elementary charge元电荷:

With e known, Thomson’s ratio gives the electron’s mass: m = e ÷ (e/m) ≈ 9.11 × 10⁻³¹ kg, about 1/1840 the mass of a hydrogen atom.

Measure a few oil drops, then use the slider to suppose a “basic charge” and see whether it divides every charge evenly:

Rutherford: the nucleus (1911)

In lesson 1.3.7, the gold-foil experiment overturned the plum pudding model. The numbers make the point even more strongly: most alpha particles went straight through the foil, and only about 1 in 8000 was deflected by more than 90°. From such data Rutherford estimated that the nucleus is about $10^{-15}$ to $10^{-14}$ m across, while the whole atom is about $10^{-10}$ m: the nucleus is roughly one hundred-thousandth the width of the atom. If an atom were blown up to the size of a football stadium, its nucleus would be an ant at the center (the comparison from lesson 1.3.2), yet it holds nearly all of the atom’s mass.

Around 1919, Rutherford showed that nuclei contain protons. In 1932, James Chadwick discovered the neutron, a neutral particle with about the same mass as a proton, which explained why most atoms have about twice as much mass as their protons alone would give.

The trouble with Rutherford’s model

According to the physics of the time, an electron circling a nucleus keeps changing direction, so it should continuously radiate electromagnetic waves, lose energy, and spiral into the nucleus in about $10^{-11}$ s. If that were true:

• atoms couldn’t be stable at all;
• the light atoms give off would contain every wavelength, a continuous spectrum.

But atoms are stable, and hydrogen gives off only a few specific colors of light (a line spectrum). In 1913, Niels Bohr proposed new rules:

• Electrons can move only in certain allowed orbits, each with a definite energy, and an electron in one of these orbits doesn’t radiate.
• An electron absorbs or emits light only when it jumps from one orbit to another, and the light’s energy equals the energy difference between the orbits.

Bohr’s model explained hydrogen’s spectrum beautifully; lessons 2.2.2 and 2.2.3 take it apart in detail.

Example 1: How much lighter is the electron?

Thomson measured the electron’s charge-to-mass ratio as 1.76 × 10¹¹ C/kg; a hydrogen ion (a proton) has a ratio of 9.58 × 10⁷ C/kg. The two charges are equal in size. What fraction of a proton’s mass is an electron’s mass?

Example 2: Finding the elementary charge

Four oil drops carry charges of 4.80, 8.01, 3.20, and 11.21 (in units of 10⁻¹⁹ C). What is the elementary charge?

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Summary

• Thomson measured the electron’s charge-to-mass ratio, e/m = 1.76 × 10¹¹ C/kg, the same for every element: electrons are part of all atoms.
• Millikan showed that charge is quantized, with elementary charge e = 1.60 × 10⁻¹⁹ C, which gives the electron’s mass as about 9.11 × 10⁻³¹ kg, roughly 1/1840 of a proton’s.
• Rutherford found that the nucleus is about one hundred-thousandth the width of the atom but holds nearly all its mass. His model couldn’t explain atomic stability or line spectra, so Bohr proposed that electrons occupy only orbits of specific energy.