The Nuclear Atom: Quick Revision

A brief note on The Nuclear Atom. Read it before a test. Try each question at the end before you open its answer.

The three particles

The nucleus

• Most alpha particles pass through gold foil; a very few bounce back. The atom is mostly empty, with a tiny, dense, positive nucleus.
• Closest approach: $d = \dfrac{2Z}{KE} \times 1.44\ \text{MeV fm}$. Radius: $R = 1.2\ \text{fm} \times A^{1/3}$.
• Every nucleus has about the same density, $2.3 \times 10^{17}\ \text{kg m}^{-3}$.

Isotopes and their cousins

Average atomic mass $=$ the sum of (mass $\times$ share). In a mass spectrometer, $r \propto \sqrt{m}$.

A worked example

Iridium is $37.3\ \%$ iridium-191 and $62.7\ \%$ iridium-193. Taking masses as mass numbers, find its average atomic mass.

1. Weight each. $191 \times 37.3 = 7124.3$ and $193 \times 62.7 = 12\,101.1$.
2. Add and divide. $\dfrac{7124.3 + 12\,101.1}{100} = 192.25\ \text{u}$.
3. Check. The answer lies between $191$ and $193$, nearer the commoner isotope.

Practice with new numbers

A program to try

The program works out the worked example.

Mistakes to avoid

• Counting electrons from the mass number. A neutral atom has $Z$ electrons; ions add or lose some.
• Mixing up isobars and isotopes. Isotopes share $Z$; isobars share $A$.
• Using $A$ in place of $A^{1/3}$ in the radius formula.
• Taking a plain average of isotope masses instead of a weighted one.

Check yourself

1. What did Millikan measure?

2. Why are most alpha particles not turned by gold foil?

3. Are carbon-14 and nitrogen-14 isotopes or isobars?

4. How many protons, neutrons and electrons does ${}^{40}_{19}\text{K}^+$ have?