Nuclear processes and changes in the nucleus

Nuclear processes are changes that occur within the nucleus of an atom, the central part containing protons and neutrons. These processes involve the release or absorption of energy and can alter the structure of the nucleus. They are fundamental to understanding how atoms behave in certain unstable states.

Types of nuclear processes:

• Fusion - This occurs when two light nuclei combine to form a heavier nucleus, releasing a large amount of energy in the process.
• Fission - This involves a heavy nucleus splitting into two or more lighter nuclei, also accompanied by the release of energy.
• Decay - This is when an unstable nucleus changes by emitting particles or radiation to become more stable, involving energy transfer.

Each of these processes results in energy transfer, often in the form of heat, light, or kinetic energy of particles.

The nature of radioactive decay

Radioactive decay is a specific type of nuclear process where an unstable nucleus spontaneously changes to become more stable. This happens by emitting particles such as alpha particles, beta particles, or gamma rays, along with energy transfer. Unlike fusion or fission, which may require external triggers, radioactive decay occurs naturally in certain isotopes.

During decay, the nucleus transforms into a different element or isotope, releasing energy that was stored in the nuclear bonds. This process is key to many natural phenomena and applications, from energy production to medical imaging.

Measuring radioactive activity in becquerels

Radioactive activity refers to the rate at which unstable nuclei in a sample undergo decay. It measures how many decay events happen over time, providing insight into the intensity of the radioactive process.

Activity is measured in becquerels (Bq), where one becquerel equals one decay per second. For example, a sample with an activity of 100 Bq experiences 100 nuclei decaying every second. This unit allows scientists to quantify and compare the decay rates of different radioactive materials.

The concept of half-life

Half-life is the time required for the number of unstable nuclei in a radioactive sample to decrease by half, or equivalently, for the activity of the sample to halve. It is a constant property for each radioactive isotope, meaning it does not change regardless of the sample size.

Half-life provides a way to predict how long a radioactive substance will remain active. For instance, if a sample starts with 1,000 unstable nuclei and has a half-life of 10 years, after 10 years, about 500 nuclei will remain undecayed, and the activity will be half of its initial value.

Patterns of exponential decay in radioactive materials

Exponential decay describes the pattern in which the number of undecayed nuclei or the activity of a radioactive sample decreases over time. This decay follows a mathematical curve where the rate of decrease is proportional to the current amount remaining.

Key characteristics of exponential decay:

• Random individual decay - Each unstable nucleus decays at a random moment, making it impossible to predict exactly when a single nucleus will decay.
• Predictable large-scale behavior - When dealing with a large number of nuclei, the overall decay rate becomes predictable and follows a consistent exponential pattern.
• Proportional decrease - The number of decays per unit time is always a fixed fraction of the remaining undecayed nuclei, leading to faster initial decay that slows over time.

This pattern results in the activity halving at regular intervals equal to the half-life, creating a curved graph when plotted against time.

Using half-life graphs to calculate decay rates

Half-life graphs plot the number of undecayed nuclei or the activity against time, showing the exponential decay curve. These graphs help visualize how the decay progresses and allow for calculations of decay rates or time intervals.

To use a half-life graph:

1. Identify the initial value (number of nuclei or activity) on the y-axis at time zero.
2. Find where the value halves on the curve to determine one half-life period.
3. Repeat for subsequent halvings to find multiple half-lives.
4. Calculate decay rates by determining the change in value over a specific time interval from the graph.

For example, if a graph shows activity dropping from 800 Bq to 200 Bq over two half-lives, the decay rate can be analyzed by noting the time for each halving.

Worked example - Calculating decay rates using a half-life graph

A half-life graph for a radioactive isotope shows an initial activity of 1,600 Bq. The activity drops to 800 Bq after 5 days and to 400 Bq after another 5 days. Calculate the half-life and the time required for the activity to reach 100 Bq.

Step 1: Identify the values

• Initial activity = 1,600 Bq
• Activity after first interval = 800 Bq (halved)
• Activity after second interval = 400 Bq (halved again)

Step 2: Determine the half-life

Each halving occurs over 5 days, so the half-life is 5 days.

Step 3: Calculate total half-lives needed

To go from 1,600 Bq to 100 Bq:

• 1,600 → 800 (1 half-life)
• 800 → 400 (2 half-lives)
• 400 → 200 (3 half-lives)
• 200 → 100 (4 half-lives)

Step 4: Compute the time

Time required = 4 half-lives × 5 days per half-life = 20 days

Therefore, the activity reaches 100 Bq after 20 days.

Applications of radiometric dating using isotope ratios and half-lives

Radiometric dating is a method that uses the known half-lives of radioactive isotopes to determine the age of materials. It relies on measuring the ratio of parent isotopes (original radioactive atoms) to daughter isotopes (products of decay) in a sample.

How radiometric dating works

1. Select an appropriate isotope pair based on the material and expected age range.
2. Measure the current ratio of parent to daughter isotopes in the sample.
3. Use the half-life to calculate how many half-lives have passed since the material formed, based on the exponential decay pattern.
4. Multiply the number of half-lives by the half-life duration to find the age.

Specific isotopes used in radiometric dating:

• Carbon-14 - Used for dating organic materials (once-living things) up to about 50,000 years old, with a half-life of 5,730 years; it works by comparing the ratio of carbon-14 to stable carbon-12.
• Uranium-238 - Applied to geological samples like rocks, effective for ages from millions to billions of years, with a half-life of 4.5 billion years; it decays through a series to lead-206, and the ratio is used for dating.

This technique assumes the initial isotope ratio is known and that no isotopes have been added or removed except through decay.

How nuclear decay remains unaffected by external conditions

Nuclear decay is a process that occurs independently of external factors, meaning the rate of decay and half-life remain constant regardless of the environment. This stability makes radioactive decay reliable for applications like dating.

External conditions that do not affect decay:

• Temperature - Changes in heat or cold do not speed up or slow down the decay rate.
• Pressure - High or low pressure environments have no impact on the nucleus's stability.
• Chemical state - Whether the atom is part of a molecule or in a pure form does not influence decay.
• Physical state - Solid, liquid, or gas phases make no difference to the decay process.

This independence arises because decay is governed solely by nuclear forces within the atom, not by external atomic or molecular interactions.