Radioactive Decay and Half-Life Quiz

Radioactive Decay

• The number of particles that decay in a given time is proportional to the total number of particles in a radioactive sample: ΔN = -λNΔt
• λ is called the decay constant and determines the rate at which the material will decay
• Decay rate or activity, R, is defined as the number of decays per second: R = ΔN / Δt = λN

Decay Curve

• The decay curve follows the equation: N = No e^(-λt)
• Half-life is defined as the time it takes for half of any given number of radioactive nuclei to decay: T1/2 = ln2 / λ ≈ 0.693 / λ

Units of Activity

• The unit of activity, R, is the Curie (Ci): 1 Ci = 3.7 x 10^10 decays/second
• The SI unit of activity is the Becquerel (Bq): 1 Bq = 1 decay/second
• 1 Ci = 3.7 x 10^10 Bq
• The most commonly used units of activity are the mCi and the µCi

Nuclear Reactions

• Structure of nuclei can be changed by bombarding them with energetic particles
• The atomic numbers and mass numbers must balance on both sides of the equation
• Example: Alpha particle colliding with nitrogen: 4He + 14N → X + 1H

Decay Series

• A decay series starts with a radioactive nucleus and ends with a stable isotope
• Example: 232Th → ... → 208Pb

Alpha Decay

• When a nucleus emits an alpha particle, it loses 2 protons and 2 neutrons: A - 4, Z - 2
• A parent nucleus (X) becomes a daughter nucleus (Y) and an alpha particle (4He)
• Example: 226Ra → 222Rn + 4He

Beta Decay

• Beta decay occurs when a neutron in the nucleus is transformed into a proton and an electron
• The emission of the electron is from the nucleus
• Energy must be conserved
• Example: A Z X → A Z+1 Y + e- + ν (electron and antineutrino emitted)

Gamma Decay

• Gamma rays are given off when an excited nucleus "falls" to a lower energy state
• Similar to the process of electron "jumps" to lower energy states and giving off photons
• Example: 12B → 12C* → 12C + γ

Mass

• A convenient unit of mass is the unified mass unit (u): 1 u = 1.660 559 x 10^-27 kg
• Mass can also be expressed in MeV/c^2: 1 u = 931.494 MeV/c^2

Size of the Nucleus

• First investigated by Rutherford in scattering experiments
• The size of the nucleus is typically measured in femtometers (fm): 1 fm = 10^-15 m
• The average radius of a nucleus is r = ro A^(1/3), where ro = 1.2 x 10^-15 m

Nuclear Stability

• The nuclear attractive force is stronger than the Coulomb repulsive force at short ranges within the nucleus
• Nuclei are stable due to the presence of the nuclear force, which acts between all nuclear particles

Stable and Unstable Isotopes

• Every element in the periodic table has at least one radioactive isotope
• Over 3300 radioisotopes are known
• Stable isotopes do not decay, while unstable isotopes do