Notes
Models of the atom
- Dalton: atoms are indivisible and identical for each element. Thomson: discovered the electron (plum pudding model). Rutherford: gold foil showed a tiny, dense, positive nucleus and mostly empty space. Bohr: electrons in energy levels. Quantum model: electrons in orbitals.
Particles and numbers
| Particle | Charge | Mass (amu) | Location |
|---|---|---|---|
| proton | +1 | 1 | nucleus |
| neutron | 0 | 1 | nucleus |
| electron | -1 | about 0 | outside nucleus |
- Atomic number $Z$ = protons. Mass number $A$ = protons + neutrons.
- Ions: cations lost electrons (+), anions gained electrons (-).
- Isotopes have the same $Z$ but different $A$. Average atomic mass $\displaystyle = \sum (\text{mass} \times \text{fractional abundance})$.
Nuclear chemistry
- Alpha ($^{4}_{2}\text{He}$): $A - 4$, $Z - 2$. Beta ($^{0}_{-1}\text{e}$): $Z + 1$. Gamma: energy only.
- Balance nuclear equations by matching total $A$ and total $Z$ on both sides.
- After $n$ half-lives, amount left $\displaystyle = \text{start} \times \left(\frac{1}{2}\right)^n$.
- Fission splits heavy nuclei; fusion joins light nuclei.
Topics in this unit
Each topic has its own short notes and practice.
Practice
$Z = 19$ protons, $39 - 19 = 20$ neutrons, and the 1+ charge means $19 - 1 = 18$ electrons.
Some alpha particles bounced back, which only a concentrated positive center could cause.
$0.600(69.0) + 0.400(71.0) = 41.4 + 28.4 = 69.8$ amu.
Mass numbers: $131 = 131 + 0$. Atomic numbers: $53 = 54 + (-1)$. That is a beta particle.
Same element means same number of protons; isotopes differ only in neutrons.
10.0 min is 5 half-lives, and $\displaystyle \left(\frac{1}{2}\right)^5 = \frac{1}{32}$.
Free response
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Free-response question
Magnesium in nature has three stable isotopes: Mg-24 (23.99 amu, 78.99%), Mg-25 (24.99 amu, 10.00%) and Mg-26 (25.98 amu, 11.01%). Magnesium's atomic number is 12.
(a) Give the number of protons, neutrons and electrons in a neutral Mg-26 atom and in a $\text{Mg}^{2+}$ ion made from Mg-26.
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Mg-26 atom: 12 protons, $26 - 12 = 14$ neutrons, 12 electrons. $\text{Mg}^{2+}$ ion: 12 protons, 14 neutrons, $12 - 2 = 10$ electrons.
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(b) Calculate the average atomic mass of magnesium.
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$0.7899(23.99) + 0.1000(24.99) + 0.1101(25.98) = 18.95 + 2.499 + 2.860 = 24.31$ amu.
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(c) Sodium-24 is radioactive. It undergoes beta decay with a half-life of 15 hours. Write the nuclear equation and find how much of a 16.0 g sample remains after 45 hours.
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$^{24}_{11}\text{Na} \rightarrow\ ^{24}_{12}\text{Mg} +\ ^{0}_{-1}\text{e}$. 45 hours is 3 half-lives: $16.0 \rightarrow 8.0 \rightarrow 4.0 \rightarrow 2.0$ g.
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