2.2 · Atomic StructurePractice · 原子结构

In the plum pudding model, positive charge is spread evenly through the whole atom, so an α particle passing through feels only a weak push and is deflected slightly at most; it could never bounce back. A few bouncing back means the positive charge and nearly all the mass sit in a tiny nucleus, which led Rutherford to the nuclear model. The other three fit the plum pudding model: atoms contain negative electrons (the beam bends toward the positive plate), the positive and negative charges balance (atoms are neutral), and every atom contains the same electrons (the same e/m).

First convert the wavelength to meters: 450 nm = 450 × 10⁻⁹ m.

Forgetting to convert nm to m makes the answer off by a factor of 10⁹.

A mole of photons is $N_A$ photons: $4.42 \times 10^{-19}\ \text{J} \times 6.022 \times 10^{23}\ \text{mol}^{-1} = 2.66 \times 10^{5}$ J/mol, about 266 kJ/mol. That’s comparable to many bond energies (a few hundred kJ/mol), which is why visible and UV light can drive some reactions.

An electron can drop straight to n = 1 or come down in steps, and each pair of levels gives its own wavelength: 4 → 3, 4 → 2, 4 → 1, 3 → 2, 3 → 1, 2 → 1, 6 in all (4 × 3 ÷ 2). The two that end at n = 2, 4 → 2 (486.3 nm) and 3 → 2 (656.5 nm), are visible; the three ending at n = 1 are ultraviolet, and 4 → 3 is infrared.

The energy released is the difference between the two levels:

That’s a violet-blue visible line, matching the measured Balmer line at 434.0 nm.

The n = 4 shell has 4 sublevels, 4s, 4p, 4d, 4f, with 1, 3, 5, 7 orbitals: 1 + 3 + 5 + 7 = 16 orbitals, which is n². Each orbital holds up to 2 electrons, so the shell holds up to 32 (2n²).

A Co atom is [Ar]4s²3d⁷. A cation loses its highest-n electrons first, the 4s electrons, not the 3d electrons that were filled last, so $\ce{Co^2+}$ is [Ar]3d⁷. [Ar]4s²3d⁵ wrongly removes 3d electrons.

Cr is an exception: [Ar]4s¹3d⁵, not 4s²3d⁴. The 3d sublevel has 5 orbitals, and by Hund’s rule its 5 electrons occupy one each with parallel spins; 4s holds 1 more. That’s 5 + 1 = 6 unpaired electrons. The half-filled 3d⁵ with 4s¹ is lower in energy.

Electrons in an ion = atomic number − charge; then check whether that matches a noble gas (2, 10, 18, 36, …). $\ce{Al^3+}$: 13 − 3 = 10, like Ne; $\ce{Zn^2+}$: 30 − 2 = 28, [Ar]3d¹⁰, no; $\ce{Sc^3+}$: 21 − 3 = 18, like Ar; $\ce{Fe^2+}$: 26 − 2 = 24, [Ar]3d⁶, no; $\ce{Se^2-}$: 34 + 2 = 36, like Kr. Transition-metal ions lose their 4s electrons but keep their 3d electrons, so $\ce{Zn^2+}$ and $\ce{Fe^2+}$ don’t have noble gas configurations.

A flame test detects elements: yellow means sodium is present, but not which sodium compound, and it says nothing about chloride. Sodium’s strong yellow hides potassium’s violet; you’d need to look through blue cobalt glass to check for potassium, so potassium may or may not be there.