Properties of Nuclear Radiation and Radioactive Decay Series

Comparison of Alpha Particles, Beta Particles, and Gamma Rays

Radiation produced during nuclear decay can be categorized into three distinct types: alpha ($\alpha$) particles, beta ($\beta$) particles, and gamma ($\gamma$) rays. Each type possesses unique physical properties, including nature, mass, charge, ionizing power, velocity, penetration capability, and behavior within electromagnetic fields. Understanding these differences is fundamental to the study of nuclear chemistry.

Alpha particles are composed of helium-4 nuclei, often represented as $^{4}_{2}He$. In terms of mass, an alpha particle is approximately four times the mass of a standard hydrogen atom. These particles carry a positive charge of double magnitude ($+2$). Due to their relatively large size and charge, alpha particles have a high capacity for ionizing the gases through which they pass. However, their physical bulk also results in low penetration or permeability, and they travel at a relatively slow velocity of approximately $0.05c$, where $c$ represents the speed of light ($c = 3 \times 10^{8}\,m/s$). When subjected to an electric field between the plates of a capacitor, alpha particles are deflected toward the negative plate due to their positive charge. In a magnetic field, they are deflected by the Lorentz force in a specific direction.

Beta particles are high-speed electrons, denoted as $^{0}_{-1}e$. Their mass is significantly smaller than that of alpha particles, being equivalent to the mass of an electron. Each beta particle carries a single negative electrical charge ($-1$). Their ability to ionize gases is notably less than that of alpha particles, but they compensate for this with much higher velocities, reaching approximately $0.9c$. Because they are smaller and faster than alpha particles, beta particles exhibit greater penetration through matter. When entering an electric field, they are deflected toward the positive plate of a capacitor. In a magnetic field, the Lorentz force causes them to deflect in a direction opposite to that of alpha particles, reflecting their opposite charge.

Gamma rays differ fundamentally from alpha and beta radiation as they are high-energy electromagnetic waves ($\gamma$) rather than particles with mass. They have no rest mass and no electrical charge. Consequently, gamma rays have the lowest ionizing power of the three types of radiation. However, they travel at the speed of light ($c = 3 \times 10^{8}\,m/s$) and possess the highest penetration capability, far exceeding that of beta particles. Because they lack an electrical charge, gamma rays are not influenced by either electric or magnetic fields and pass through them without any deflection.

Radioactive Decay Series

Radioactive nuclei do not always reach stability in a single step. Instead, they transform through a sequence of successive nuclear reactions known as a radioactive decay series. In such a series, a parent radioactive nucleus undergoes a chain of transformations, producing various intermediate nuclei until a final stable nucleus is reached. This process continues through either alpha or beta emissions (or both) until the nuclear configuration reaches a state of stability.

Application: Uranium-238 to Lead-206 Decay Series

A classic example of a radioactive decay series is the transformation of radioactive Uranium-238 ($^{238}_{92}U$) into stable Lead-206 ($^{206}_{82}Pb$). This process involves the emission of a specific number of alpha particles ($x$) and beta particles ($y$), along with the release of energy. The overall nuclear equation for this transformation is represented as:

$^{238}_{92}U \rightarrow x\,^{4}_{2}He + y\,^{0}_{-1}e + ^{206}_{82}Pb + \text{Energy}$

To determine the number of alpha transformations ($x$) and beta transformations ($y$), we apply the laws of conservation of mass and conservation of atomic number (charge). First, we calculate $x$ by balancing the mass numbers (top numbers) from the reactants to the products:

$238 = 4x + (y \times 0) + 206$

$238 = 4x + 206$

$32 = 4x$

$x = 8$

This indicates that the decay of Uranium-238 to Lead-206 involves the emission of 8 alpha particles. Next, we calculate $y$ by balancing the atomic numbers (bottom numbers), using the value of $x$ we just found:

$92 = (2 \times x) + (-1 \times y) + 82$

$92 = (2 \times 8) - y + 82$

$92 = 16 - y + 82$

$92 = 98 - y$

$y = 98 - 92$

$y = 6$

This indicates that 6 beta particles are emitted during the series. The complete and balanced nuclear equation for this decay series is:

$^{238}_{92}U \rightarrow 8\,^{4}_{2}He + 6\,^{0}_{-1}e + ^{206}_{82}Pb + \text{Energy}$