Vocabulary & Radioactive Decay

What is an isotope?

Atoms of the same element with the same number of protons but different numbers of neutrons.

What determines nuclear stability?

The neutron-to-proton (n:p) ratio; small nuclei are stable near 1:1, larger nuclei require more neutrons to offset proton repulsion.

Why do isotopes undergo radioactive decay?

To achieve a more stable neutron-to-proton ratio when outside the band of stability.

What force holds the nucleus together?

The strong nuclear force, which counteracts proton–proton repulsion.

How many stable isotopes exist naturally on Earth?

About 250; all isotopes beyond lead (Pb) are radioactive.

What is fission?

Splitting a large unstable nucleus into smaller nuclei, releasing large amounts of energy.

What is fusion?

Combining small nuclei into a larger nucleus in a highly exothermic process (as in stars).

What is radioactive decay?

Transformation of an unstable nucleus into a more stable one through emission of radiation.

Rank the typical energies in nuclear, chemical, and intermolecular processes.

Nuclear: millions–billions kJ/mol; chemical bonds: hundreds–thousands kJ/mol; intermolecular forces: tens of kJ/mol.

What type of kinetics describes radioactive decay?

First-order kinetics; decay rate depends only on the amount of radioactive nucleus.

What is half-life?

Time required for half of a radioactive sample to decay.

After 3 half-lives, what fraction remains?

One-eighth (12.5%).

What occurs during alpha decay?

Emission of a helium-4 nucleus; atomic number −2, mass number −4.

What occurs during beta-minus decay?

A neutron converts to a proton and an electron is emitted; atomic number +1, mass number unchanged.

What occurs during beta-plus decay (positron emission)?

A proton converts to a neutron; a positron is emitted; atomic number −1, mass number unchanged.

What occurs during gamma decay?

Emission of a high-energy photon with no change in atomic number or mass number.

Which type of decay has the highest penetration power?

Gamma decay.

²³⁸₉₂U → ?

Alpha decay (loss of a helium nucleus).

Strontium-89 → yttrium-89 + electron

Beta-minus decay (neutron → proton).

Sodium-22 → neon-22 + positron

Beta-plus decay (positron emission).

Cobalt-60 → nickel-60 + γ photon

Gamma decay (photon emission).

Polonium-210 → lead-206 + helium-4

Alpha decay.

Half-life problem: 640 mg, 24 days (t½ = 12 days)

Two half-lives → 160 mg remain.

Half-life problem: 800 g, 10 hours (t½ = 5 hours)

Two half-lives → 200 g remain.

Half-life problem: 100 g, 8 days (t½ = 4 days)

25 g remain.

¹⁴C decays 11,460 years (2 half-lives).

1/4 (25%) remains.

If 25 g remain after 3 half-lives, what was the original mass?

25 g × 2³ = 200 g.