Beta Decay: Videos & Practice Problems

Beta decay occurs when an unstable nucleus emits a beta particle, which is an electron with negligible mass and an atomic number of -1. For example, in the decay of mercury-201 (atomic number 80), the emission of a beta particle transforms it into thallium-201 (atomic number 81). Beta particles are smaller than alpha particles, resulting in lower ionizing power but greater penetrating ability, requiring a sheet of metal or a large block of wood for protection against them.

Beta Decay Concept 1

Beta decay is a type of radioactive decay that occurs when an unstable atomic nucleus emits a beta particle, which is essentially an electron. In this context, the beta particle can be represented by the symbol \( e^- \). The electron has an atomic mass that is negligible, often approximated as 0, and its atomic number is -1, reflecting its negative charge, which is the opposite of a proton's positive charge (atomic number +1).

To illustrate beta decay, consider the example of mercury-201 (\( \text{Hg}_{80}^{201} \)). In this case, the atomic mass of mercury is 201, and its atomic number is 80. When mercury-201 undergoes beta decay, it emits a beta particle. The conservation of atomic mass and atomic number must be maintained in the decay process. Since the emitted electron has no mass, the mass of the resulting element remains 201. However, the atomic number changes due to the emission of the electron.

To determine the new atomic number after the emission, we can set up the equation: \( 80 + (-1) = 81 \). This means that the new element formed after the beta decay will have an atomic number of 81, which corresponds to thallium (Tl). Therefore, the complete representation of this beta decay can be written as:

\[ \text{Hg}_{80}^{201} \rightarrow \text{Tl}_{81}^{201} + e^- \]

This equation illustrates the process of beta decay, where mercury-201 transforms into thallium-201 while emitting a beta particle (electron).

Beta Decay Concept 2

In the study of radioactive particles, alpha particles are recognized as the largest type, which influences their behavior and effects on matter. In contrast, beta particles are smaller, leading to a lower ionizing power. This means that if beta particles are ingested, they are generally less damaging compared to alpha particles. However, their smaller size allows beta particles to penetrate materials more effectively, including human skin. As a result, while they are less ionizing, they possess greater penetrating power.

To effectively shield against beta particles, a sheet of metal or a large block of wood is required. This is crucial for preventing beta particles from entering the body, highlighting the importance of understanding the properties of different radioactive particles in terms of safety and protection.

Beta Decay Example 1

In nuclear chemistry, beta decay is a process where a beta particle (an electron or positron) is emitted from an atomic nucleus. This emission results in a transformation of the original element into a new element while maintaining the same atomic mass. Understanding how to write balanced nuclear equations for beta emissions is crucial for studying radioactive decay.

For example, consider magnesium-25, which has an atomic mass of 25 and an atomic number of 12. During beta decay, magnesium-25 emits a beta particle, resulting in the formation of a new element. The atomic mass remains unchanged at 25, while the atomic number increases by one. This can be represented as:

$$^{25}_{12}\text{Mg} \rightarrow ^{25}_{13}\text{Al} + \beta^-$$

Here, the new element formed is aluminum (Al), with an atomic number of 13. The beta particle is denoted as $$\beta^-$$, indicating the emission of an electron.

Another example involves ruthenium-102, which has an atomic mass of 102 and an atomic number of 44. Upon emitting a beta particle, the atomic mass remains 102, but the atomic number increases to 45, leading to the formation of rhodium (Rh). This can be expressed as:

$$^{102}_{44}\text{Ru} \rightarrow ^{102}_{45}\text{Rh} + \beta^-$$

In both cases, the key takeaway is that during beta decay, the atomic mass remains constant while the atomic number increases by one, resulting in the formation of a new element. This fundamental concept is essential for understanding the behavior of radioactive isotopes and their transformations.

Beta Decay Example 2

In the process of nuclear decay, understanding the transformations that occur during alpha and beta decay is crucial for solving problems related to the formation of new elements. In this scenario, we start with Thorium-232, which has an atomic number of 90, and we need to determine how many alpha and beta decays have occurred to produce Lead-208, with an atomic number of 82.

Alpha decay involves the emission of an alpha particle, which consists of 2 protons and 2 neutrons (essentially a helium nucleus). This process results in a decrease of the atomic mass by 4 and the atomic number by 2. Therefore, for each alpha decay, the element loses 4 units of mass and 2 units of atomic number. Conversely, beta decay involves the emission of a beta particle, represented as \( \frac{0}{-1} e \), which increases the atomic number by 1 without affecting the atomic mass.

To find the total number of decays, we first calculate the change in atomic mass from Thorium-232 to Lead-208. The difference is:

\( 232 - 208 = 24 \)

This indicates a total loss of 24 in atomic mass. Since each alpha decay results in a loss of 4, we can determine the number of alpha decays:

\( \frac{24}{4} = 6 \)

Thus, 6 alpha decays must have occurred, leading to a new element with an atomic number of:

\( 90 - (6 \times 2) = 78 \)

This corresponds to Platinum (atomic number 78). Next, to convert Platinum into Lead, we need to increase the atomic number from 78 to 82, which requires:

\( 82 - 78 = 4 \)

Since each beta decay increases the atomic number by 1, we conclude that 4 beta decays are necessary.

In summary, the transformation from Thorium-232 to Lead-208 involves 6 alpha decays and 4 beta decays. The overall reaction can be represented as:

\( \text{Thorium-232} \rightarrow \text{Lead-208} \)

with the equation:

\( \text{232}_{90}\text{Th} \rightarrow \text{208}_{82}\text{Pb} \) (6 alpha decays + 4 beta decays)

Understanding the effects of alpha and beta decay on atomic mass and atomic number is essential for solving nuclear decay problems effectively.

Here’s what students ask on this topic:

What is beta decay and how does it occur?

Beta decay is a type of radioactive decay in which an unstable nucleus emits a beta particle, which is an electron. This process occurs when a neutron in the nucleus transforms into a proton and an electron. The electron, known as the beta particle, is then emitted from the nucleus. The atomic number of the element increases by one, while the atomic mass remains unchanged. For example, in the decay of mercury-201 (atomic number 80), the emission of a beta particle transforms it into thallium-201 (atomic number 81).

What are the differences between alpha and beta particles?

Alpha particles are larger and consist of two protons and two neutrons, making them more massive than beta particles, which are simply electrons. Due to their larger size, alpha particles have higher ionizing power but lower penetrating ability. They can be stopped by a sheet of paper or human skin. In contrast, beta particles have lower ionizing power but greater penetrating ability, requiring a sheet of metal or a large block of wood for protection. This makes beta particles more capable of penetrating the skin and potentially causing internal damage.

How does beta decay affect the atomic number and mass number of an element?

In beta decay, the atomic number of the element increases by one, while the mass number remains unchanged. This is because a neutron in the nucleus is converted into a proton and an electron (the beta particle). The proton remains in the nucleus, increasing the atomic number by one, while the electron is emitted. For example, when mercury-201 (atomic number 80) undergoes beta decay, it transforms into thallium-201 (atomic number 81), with the mass number staying at 201.

What materials can stop beta particles?

Beta particles, being smaller and less massive than alpha particles, have greater penetrating power. To stop beta particles, materials such as a sheet of metal (e.g., aluminum) or a large block of wood are required. These materials are dense enough to absorb the energy of the beta particles and prevent them from penetrating further. Unlike alpha particles, beta particles can penetrate human skin, so adequate shielding is necessary to protect against their potential harmful effects.

Why do beta particles have lower ionizing power compared to alpha particles?

Beta particles have lower ionizing power compared to alpha particles because they are much smaller and carry less charge. Alpha particles consist of two protons and two neutrons, making them highly charged and massive, which allows them to ionize atoms more effectively as they pass through matter. In contrast, beta particles are simply electrons with a single negative charge and much less mass. This lower charge and mass result in fewer interactions with atoms, leading to lower ionizing power. However, their smaller size gives them greater penetrating ability.