Radioactivity & Radioactive Decay


Radioactivity is a fundamental concept in nuclear physics, involving the spontaneous emission of particles and energy from the nucleus of an atom. This phenomenon is observed in certain isotopes, known as radioisotopes, which are forms of an element with the same number of protons but a different number of neutrons.

These isotopes can be stable or unstable; the instability arises from an imbalance in the number of protons and neutrons within the nucleus. To achieve stability, these unstable nuclei undergo radioactive decay, a process during which they emit particles and energy.

Henri Becquerel’s Discovery

The discovery of radioactivity dates back to 1896, when Henri Becquerel, while investigating phosphorescence in uranium salts, accidentally found that these salts emitted radiation that could expose photographic plates, a property unrelated to their phosphorescent behavior. This serendipitous discovery revealed that uranium, and subsequently other elements, spontaneously emitted radiation without any external source of energy.

Randomness of Radioactive Emissions

A notable characteristic of radioactivity is its inherent randomness. The decay of radioactive atoms is not influenced by external conditions such as temperature, pressure, or chemical state.

Every nucleus of a radioactive substance has the same probability of decaying, but it is impossible to predict which specific nucleus will decay next or when it will happen. Despite this randomness, the average behavior of a large number of radioactive atoms can be described by statistical laws, allowing scientists to predict the decay pattern of a radioactive sample over time.

Types of Radioactive Emissions

Radioactive emissions can take several forms, primarily alpha particles, beta particles, and gamma rays. Each type of emission has distinct properties and effects on the atom from which it originates:

  • Alpha Particles are helium nuclei, consisting of two protons and two neutrons. When an atom emits an alpha particle, its atomic number decreases by two and its mass number decreases by four, transforming into a different element. For example, when radium-226 decays, it emits an alpha particle to become radon-222.
  • Beta Particles are high-energy, high-speed electrons (β-) or positrons (β+) emitted from a nucleus. Beta decay changes the atomic number of the nucleus by one, either increasing or decreasing it, while the mass number remains unchanged. This transformation occurs as a neutron in the nucleus converts into a proton (or vice versa), emitting a beta particle in the process. An example of beta decay is when carbon-14 transforms into nitrogen-14.
  • Gamma Rays are high-energy electromagnetic waves emitted from the nucleus. Gamma emission often accompanies alpha or beta decay, as the nucleus rearranges into a more stable state and releases excess energy in the form of gamma radiation. Gamma rays do not alter the atomic or mass numbers of the emitting nucleus.

Radioactive Decay

Radioactive decay is a fundamental process in nuclear physics, characterized by the transformation of an unstable nucleus into a more stable configuration. This transformation involves the emission of particles and energy, leading to the conversion of one element into another. The nucleus that undergoes decay is known as the “parent” nucleus, while the resulting, more stable nucleus is termed the “daughter” nucleus. This process is crucial for understanding both the natural behavior of elements and their applications in various scientific fields.

Mechanism of Radioactive Decay

Radioactive decay occurs when a nucleus contains an imbalance in the number of protons and neutrons, making it unstable. To achieve stability, the nucleus releases energy and particles, which can include alpha (α) particles, beta (β) particles, and gamma (γ) rays. Each type of emission alters the nucleus in distinct ways:

Alpha Decay

In this process, the parent nucleus emits an alpha particle, which is essentially a helium-4 nucleus. An alpha particle can be represented as  $^{4}_{2} He$ or $^{4}_{2} \alpha$. This emission results in a decrease of two in the atomic number (Z) and four in the mass number (A), leading to a significant transformation of the parent element into a different daughter element.

$$^{A}_{Z}X \rightarrow ^{A-4}_{Z-2}Y + ^{4}_{2}He + \text{energy}$$

Example: $^{226}_{88}Ra \rightarrow ^{222}_{86}Rn + ^{4}_{2}He + \text{energy}$

Beta Decay

Beta decay occurs through the emission of beta particles, which can be electrons (β-) or positrons (β+). In nuclear equation, β-particles is written as $^{0}_{-1} \beta$ or $^{0}_{-1} e$. This process changes the atomic number by one, either increasing or decreasing it, but leaves the mass number unchanged. Beta decay signifies a transformation within the nucleus where a neutron converts into a proton (or vice versa), facilitating the conversion of the parent element into a different daughter element.

  • During this process, a neutron splits into a proton, an electron and a positron (which decays rapidly into pure energy). The proton number now increases. The new electron is expelled as β-particles.

$$^{A}_{Z}X \rightarrow ^{A}_{Z+1}Y + ^{0}_{-1}e + \text{energy}$$

Example: $^{24}_{11}Na \rightarrow ^{24}_{12}Mg + ^{0}_{-1}\beta + \text{energy}$

Gamma Emission

Following alpha or beta decay, a nucleus may still be in an excited energy state. It can then transition to a lower energy state by emitting a gamma ray, a form of high-energy electromagnetic radiation. Gamma emission does not change the atomic or mass numbers but rather moves the nucleus to a more stable energy state.

γ-rays are usually emitted at the same time as α-particles and β-particles. With some nuclides, the emission of α-particles and β-particles from a nucleus leaves the electrons and neutrons in an excited arrangement with more energy than normal. These protons and neutrons rearrange themselves to become more stable and release the excess energy as a photon of gamma radiation.

Characteristics of Radioactive Decay

  • Spontaneous Process: Radioactive decay is an autonomous process that occurs without any external influence. The rate of decay is not affected by environmental conditions such as temperature, pressure, or the chemical state of the material. This intrinsic property underscores the stability considerations of atomic nuclei.
  • Random Process: The decay of individual nuclei is unpredictable and random. Although each parent nucleus within a sample has the same probability of decaying, it is impossible to determine which nucleus will decay next and at what time. This randomness is a fundamental aspect of quantum mechanics and nuclear physics.

Observing Randomness

The randomness of radioactive decay can be empirically observed using instruments like the Geiger-Müller (GM) tube, which detects the presence of ionizing radiation. When placed near a radioactive source, the GM tube records the emission of particles and energy as discrete counts. The fluctuating count rate not only demonstrates the randomness of decay events but also provides a quantitative measure of the decay process.

Implications and Applications

Understanding radioactive decay has profound implications for a wide range of scientific and practical applications. It is essential for nuclear medicine, radiometric dating, nuclear energy production, and the study of environmental radioactivity. Moreover, the principles of radioactive decay contribute to our understanding of the universe’s age, the formation of elements in stars, and the dynamics of atomic and molecular structures.

Background Radiation

Background radiation is the natural environmental radiation that surrounds us.

  • Existence: The G-M tube usually detects 20 to 60 counts per minute without a radioactive source. This is due to background radiation.

It originates from various sources, including cosmic rays, terrestrial sources like rocks and soil containing radioactive materials, and even from within our own bodies due to the presence of naturally occurring radioactive isotopes. Additionally, human-made sources such as medical treatments, nuclear power plants, and industrial activities contribute to background radiation levels.

The presence of background radiation is a constant reminder of the pervasive nature of radioactivity, and it plays a crucial role in fields such as environmental science, radiology, and nuclear physics.

  • Significance: Natural radioactive elements produce a radioactive gas, radon, which may accumulate in buildings, so increasing the local background count. Whenever taking readings with GM tube, the background count should be established at the start and deducted from subsequent readings to avoid systematic error.

Understanding radioactivity and radioactive decay is crucial for numerous applications, including medical treatments (radiation therapy), radiocarbon dating for archaeological discoveries, nuclear energy production, and safety assessments for radiation exposure. The study of radioactivity not only unveils the atomic structure and the forces within the nucleus but also provides insights into the age of Earth, the evolution of stars, and the origins of the elements in the universe.

Worked Examples

Example 1

A radioactive nuclide emits an alpha particle and two beta particles. Compared with the original nuclide, the resulting nuclide will have

  1. the same nucleon number
  2. a higher proton number
  3. a lower proton number
  4. the same proton number
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Nucleon number will be lower but proton number unchanged.

Answer: 4

Example 2: Identifying Radioactive Emissions

Question: A certain isotope undergoes radioactive decay and emits a particle that increases its atomic number by 1 without changing its mass number. What type of particle did it most likely emit?

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Answer: The isotope emitted a beta particle (β-). In beta decay, a neutron in the nucleus is transformed into a proton, and a beta particle (electron) is emitted. This process increases the atomic number by 1 (due to the addition of a proton) but leaves the mass number unchanged, as both protons and neutrons contribute to the mass number and their total count remains the same.

Example 3: Calculating Decay Products

Question: Uranium-238, with 92 protons, undergoes alpha decay. What are the atomic number and mass number of the daughter nucleus?

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Answer: In alpha decay, the atomic number decreases by 2 and the mass number decreases by 4. Uranium-238 (atomic number = 92) emitting an alpha particle would result in a daughter nucleus with an atomic number of 90 and a mass number of 234. This corresponds to the element thorium (Th).

Example 4: Understanding Gamma Emission

Question: After undergoing beta decay, a nucleus emits a gamma ray. What changes occur to the atomic and mass numbers of the nucleus?

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Answer: The emission of a gamma ray does not change the atomic or mass numbers of a nucleus. Gamma rays are high-energy photons emitted as a nucleus transitions from a higher to a lower energy state. This process occurs without altering the composition of the nucleus, meaning the atomic and mass numbers remain unchanged.

Example 5: Background Radiation Count Adjustment

Question: If the background radiation count is 40 counts per minute (cpm) and a radioactive sample registers 240 cpm using a Geiger-Müller tube, what is the net count rate from the sample?

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Answer: To find the net count rate from the sample, subtract the background radiation count from the total count observed with the sample. Net count rate = 240 cpm – 40 cpm = 200 cpm.

Example 6: Predicting Daughter Elements

Question: Carbon-14 undergoes beta decay to form a new element. Identify the daughter element and its atomic number.

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Answer: In beta decay, the atomic number increases by 1 while the mass number remains unchanged. Carbon-14 (atomic number 6) undergoing beta decay results in a daughter element with an atomic number of 7, which is nitrogen (N-14).

Example 7: Alpha Particle Emission and Element Transformation

Question: Radium-226, with 88 protons, emits an alpha particle. Write the nuclear equation for this decay and identify the daughter element.

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Answer: Radium-226 (Ra-226) emitting an alpha particle ($\text{He}_2^4$) results in a decrease of 2 in the atomic number and 4 in the mass number. The nuclear equation is:

$$\text{Ra}_{88}^{226} \rightarrow \text{Rn}_{86}^{222} + \text{He}_2^4$$

The daughter element is radon-222 (Rn-222).

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