Radioactive Isotopes and Decay

Radioisotopes

• Radioactive isotopes (radioisotopes) have unstable nuclei.
• They undergo spontaneous radioactive decay to become more stable.
• This process emits radiation, either:
  • High-energy particles (alpha particles).
  • High-energy electromagnetic radiation (gamma rays).
• There are over 300 naturally occurring isotopes, but only 36 are radioisotopes.
• All isotopes with an atomic number greater than 82 are radioactive.
• There are also over 2,000 man-made (artificial) radioisotopes.
• Artificial radioisotopes are used in smoke detectors, computer monitors, and medical imaging.
• Most daily radiation exposure is from natural sources (background radiation).
  • Examples: cosmic rays, radon gas.
  • Our bodies contain small amounts of radioisotopes like Carbon-14.

Radioactive Decay

• Unstable parent isotopes break down into stable daughter isotopes (daughter nuclei).
• Radioactive isotopes emit:
  • High-energy particles (alpha or beta particles).
  • High-energy radiation (gamma rays or X-rays).

Alpha Decay

• Alpha decay is the emission of an alpha particle.
• An alpha particle consists of two protons and two neutrons (no electrons).
• It has a +2 charge due to the two protons.
• Nuclear symbol: $^{4}_{2}\alpha$
  • Subscript 2: number of protons (atomic number).
  • Superscript 4: mass number (sum of protons and neutrons).
• Alpha emission releases a new, more stable, smaller nucleus (daughter nucleus).
• The original unstable nucleus is the parent nucleus.
• The daughter nucleus has:
  • Mass number 4 less than the parent.
  • Atomic number 2 less than the parent.
• Sometimes the daughter nucleus is also radioactive and undergoes further decay.

Nuclear Equations for Alpha Decay

• Represents radioactive decay using nuclear symbols.
• Parent nucleoid on the left, arrow indicating formation of daughter nuclei and emitted particle on the right.
• Example: Alpha decay of Radium-223 (used in prostate cancer treatment).
• $^{223}<em>{88}Ra \rightarrow ^{219}</em>{86}Rn + ^{4}_{2}\alpha$
• Atomic numbers and mass numbers are shown as subscripts and superscripts.
• Equation must be balanced:
  • Atomic number (parent) = sum of atomic numbers (daughter + emitted particle).
  • Mass number (parent) = sum of mass numbers (daughter + emitted particle).

Problem Example: Alpha Decay of Radium-226

• Write a balanced nuclear equation for the alpha decay of Radium-226.
• Radium (Ra) is the parent nucleoid, so it's on the left side of the arrow.
• Mass number (226) is the superscript.
• Atomic number of radium (88) is found on the periodic table.
• $^{226}<em>{88}Ra \rightarrow X + ^{4}</em>{2}\alpha$
• Alpha particle atomic number is 2, mass number is 4.
• To find the daughter nuclei (X):
  • Atomic number: 88 = A + 2, so A = 86.
  • Mass number: 226 = B + 4, so B = 222.
• Element with atomic number 86 is Radon (Rn).
• Balanced equation: $^{226}<em>{88}Ra \rightarrow ^{222}</em>{86}Rn + ^{4}_{2}\alpha$

Beta Decay

• Beta decay occurs when a radioisotope emits a beta particle.
• A beta particle is a high-energy electron traveling at 90% the speed of light.
• Nuclear symbol: $^{0}_{-1}\beta$
  • No mass number (0).
  • Atomic number is -1.
• Beta emission produces a daughter nucleoid with:
  • Same mass number as the parent.
  • Atomic number one greater than the parent.
• Example: Carbon-14 decay.

Nuclear Equations for Beta Decay

• Example: P-32 (used in breast cancer and eye tumor detection).
• $^{32}<em>{15}P \rightarrow ^{32}</em>{16}S + ^{0}_{-1}\beta$
• The daughter nucleoid (Sulfur) has an atomic number one greater than the parent (Phosphorus).
• Mass number remains the same.

Problem Example: Beta Decay of Gold-198

• Write the nuclear equation for the beta decay of Gold-198 (beta emitter).
• Gold (Au) is the parent nuclei.
• Atomic mass number is 198; atomic number (from periodic table) is 79.
• $^{198}<em>{79}Au \rightarrow X + ^{0}</em>{-1}\beta$
• In beta emission, the mass number remains the same.
• Atomic number increases by one (79 + 1 = 80).
• Element with atomic number 80 is Mercury (Hg).
• $^{198}<em>{79}Au \rightarrow ^{198}</em>{80}Hg + ^{0}_{-1}\beta$

Gamma Ray Emission

• Most radioactive decays include gamma rays along with alpha or beta particles.
• Gamma rays do not change atomic number or mass number.
• Gamma rays are pure energy.
• Symbol: $^0_0\gamma$
• Parent nuclei is shown with