Question

What changes in atomic number and mass number occur in each of the following types of radioactive decay? a. alpha emission b. beta emission c. positron emission d. electron capture

Short answer

Alpha: Atomic number -2, Mass number -4. Beta: Atomic number +1, Mass number unchanged. Positron: Atomic number -1, Mass number unchanged. Electron capture: Atomic number -1, Mass number unchanged.

Step-by-step solution

Understand Alpha Emission

Alpha emission occurs when an unstable nucleus emits an alpha particle, which consists of 2 protons and 2 neutrons. As a result, the atomic number decreases by 2 (since the nucleus loses 2 protons) and the mass number decreases by 4 (since the nucleus loses 2 protons and 2 neutrons).

Understand Beta Emission

Beta emission occurs when a neutron in an unstable nucleus is converted into a proton and an electron. The electron (beta particle) is emitted from the nucleus. Consequently, the atomic number increases by 1 (since a neutron converts to a proton), but the mass number remains unchanged.

Understand Positron Emission

Positron emission occurs when a proton in an unstable nucleus is converted into a neutron and a positron. The positron is emitted from the nucleus. As a result, the atomic number decreases by 1 (since a proton converts to a neutron), while the mass number remains unchanged.

Understand Electron Capture

Electron capture happens when an electron from an atom's inner shell is captured by the nucleus, causing a proton to convert into a neutron. This decreases the atomic number by 1 (since a proton becomes a neutron), but the mass number stays the same.

Key concepts

alpha emission

Alpha emission occurs when an unstable nucleus releases an alpha particle, which consists of 2 protons and 2 neutrons. This kind of particle is symbolized as \(_{2}^{4}He\), and it is also known as a helium-4 nucleus.

When a nucleus undergoes alpha emission:
- The atomic number (Z) decreases by 2 because it loses 2 protons
- The mass number (A) decreases by 4 because it loses a total of 4 nucleons (2 protons and 2 neutrons)

For example, during the alpha decay of Uranium-238 (\(_{92}^{238}U\)), the reaction can be expressed as:

\(_{92}^{238}U \rightarrow _{90}^{234}Th + _{2}^{4}He\)

This shows the decrease in atomic number and mass number due to the emission of the alpha particle.

beta emission

Beta emission happens when a neutron in an unstable nucleus is transformed into a proton and an electron. The electron, also known as a beta particle, is then emitted from the nucleus.

In beta emission:
- The atomic number (Z) increases by 1 because a neutron turns into a proton
- The mass number (A) remains unchanged because the total number of nucleons is the same

The formula for this process can be represented as:

\(_{0}^{1}n \rightarrow _{1}^{1}p + _{-1}^{0}e\)

A practical example is the beta decay of Carbon-14 (\(_{6}^{14}C\)), which can be written as:

\(_{6}^{14}C \rightarrow _{7}^{14}N + _{-1}^{0}e\)

This equation illustrates the change in atomic number without altering the mass number.

positron emission

Positron emission occurs when a proton in an unstable nucleus is converted into a neutron and a positron. The positron, a particle with the same mass as an electron but with a positive charge, is expelled from the nucleus.

During positron emission:
- The atomic number (Z) decreases by 1 because a proton turns into a neutron
- The mass number (A) remains unchanged as the number of nucleons doesn't change

This process can be represented as:

\(_{1}^{1}p \rightarrow _{1}^{0}n + _{1}^{0}e\)

An example of positron emission can be seen with Fluorine-18 (\(_{9}^{18}F\)), which decays as:

\(_{9}^{18}F \rightarrow _{8}^{18}O + _{1}^{0}e\)

This equation shows how the atom's proton changes to a neutron, producing a positron and lowering the atomic number by one.

electron capture

Electron capture is an event where an inner-shell electron is absorbed by the nucleus of an atom. This captured electron combines with a proton to form a neutron.

In electron capture:
- The atomic number (Z) decreases by 1 as a proton is converted into a neutron
- The mass number (A) remains the same because the total number of nucleons does not change

The process is generally represented as:

\(_{p} + e^{-} \rightarrow _{n}\)

An example would be the electron capture by Beryllium-7 (\(_{4}^{7}Be\)), written as:

\(_{4}^{7}Be + e^{-} \rightarrow _{3}^{7}Li\)

This equation illustrates how the atomic number is decreased by one as an electron is captured and a proton becomes a neutron, without impacting the mass number.