Determining the Resulting Nuclide

Oct 13, 2025 by miodeya.com 145 views

Understanding Radioactive Decay: The Case of ${}^{210}Pb$

Radioactive decay is a process in which unstable atomic nuclei lose energy by emitting radiation in the form of particles or electromagnetic waves. This process is a key aspect of nuclear physics and has numerous applications in fields such as medicine, energy production, and materials science. In this article, we will delve into the specifics of radioactive decay, focusing on the case of ${}^{210}Pb$ , a radioactive isotope of lead that decays by emitting a $\beta^{-}$ particle.

What is Radioactive Decay?

Radioactive decay is a spontaneous process in which an unstable nucleus loses energy by emitting radiation. This radiation can take various forms, including alpha particles ( $\alpha$ ), beta particles ( $\beta$ ), and gamma rays ( $\gamma$ ). The type of radiation emitted depends on the specific isotope undergoing decay.

Beta Decay

Beta decay is a type of radioactive decay in which a neutron in the nucleus is converted into a proton, an electron ( $\beta^{-}$ ), and a neutrino. This process is represented by the following equation:

$n \rightarrow p + \beta^{-} + \nu$

In this equation, $n$ represents a neutron, $p$ represents a proton, $\beta^{-}$ represents a beta particle (an electron), and $\nu$ represents a neutrino.

The Case of ${}^{210}Pb$

${}^{210}Pb$ is a radioactive isotope of lead that decays by emitting a $\beta^{-}$ particle. This means that a neutron in the nucleus of ${}^{210}Pb$ is converted into a proton, an electron, and a neutrino. The resulting nuclide has one more proton than the original nuclide, but the same number of neutrons.

Determining the Resulting Nuclide

To determine the resulting nuclide, we need to consider the changes in the atomic number (number of protons) and mass number (total number of protons and neutrons) of the nucleus. In the case of ${}^{210}Pb$ , the atomic number is 82 (lead) and the mass number is 210.

When a neutron is converted into a proton, the atomic number increases by one, but the mass number remains the same. Therefore, the resulting nuclide has an atomic number of 83 and a mass number of 210.

The Resulting Nuclide

The resulting nuclide with an atomic number of 83 and a mass number of 210 is ${}^{210}Bi$ . Bismuth is a chemical element with the symbol Bi and atomic number 83.

Conclusion

In conclusion, ${}^{210}Pb$ decays by emitting a $\beta^{-}$ particle, resulting in the production of ${}^{210}Bi$ . This process is a classic example of beta decay, in which a neutron is converted into a proton, an electron, and a neutrino. Understanding radioactive decay and the resulting nuclides is crucial in various fields, including nuclear physics, chemistry, and materials science.

Key Takeaways

Radioactive decay is a process in which unstable atomic nuclei lose energy by emitting radiation.
Beta decay is a type of radioactive decay in which a neutron is converted into a proton, an electron, and a neutrino.
${}^{210}Pb$ decays by emitting a $\beta^{-}$ particle, resulting in the production of ${}^{210}Bi$ .
Understanding radioactive decay and the resulting nuclides is crucial in various fields, including nuclear physics, chemistry, and materials science.

Frequently Asked Questions

Q: What is radioactive decay? A: Radioactive decay is a process in which unstable atomic nuclei lose energy by emitting radiation.
Q: What is beta decay? A: Beta decay is a type of radioactive decay in which a neutron is converted into a proton, an electron, and a neutrino.
Q: What is the resulting nuclide of ${}^{210}Pb$ decay? A: The resulting nuclide of ${}^{210}Pb$ decay is ${}^{210}Bi$ .

References

[1] Wikipedia: Radioactive decay
[2] Wikipedia: Beta decay
[3] IAEA: Radioactive decay
[4] Chemistry LibreTexts: Radioactive decay

Further Reading

Radioactive decay: A comprehensive review
Beta decay: A detailed explanation
Nuclear physics: A textbook for students
Chemistry: A textbook for students
Q&A: Radioactive Decay and ${}^{210}Pb$

In our previous article, we explored the concept of radioactive decay and the specific case of ${}^{210}Pb$ decaying by emitting a $\beta^{-}$ particle. In this article, we will answer some frequently asked questions related to radioactive decay and ${}^{210}Pb$ .

Q: What is radioactive decay?

A: Radioactive decay is a process in which unstable atomic nuclei lose energy by emitting radiation. This radiation can take various forms, including alpha particles ( $\alpha$ ), beta particles ( $\beta$ ), and gamma rays ( $\gamma$ ).

Q: What is beta decay?

A: Beta decay is a type of radioactive decay in which a neutron in the nucleus is converted into a proton, an electron ( $\beta^{-}$ ), and a neutrino. This process is represented by the following equation:

$n \rightarrow p + \beta^{-} + \nu$

Q: What is the resulting nuclide of ${}^{210}Pb$ decay?

A: The resulting nuclide of ${}^{210}Pb$ decay is ${}^{210}Bi$ . This is because the atomic number of ${}^{210}Pb$ is 82 (lead) and the mass number is 210. When a neutron is converted into a proton, the atomic number increases by one, but the mass number remains the same. Therefore, the resulting nuclide has an atomic number of 83 and a mass number of 210, which is ${}^{210}Bi$ .

Q: What is the half-life of ${}^{210}Pb$ ?

A: The half-life of ${}^{210}Pb$ is approximately 22.3 years. This means that every 22.3 years, the amount of ${}^{210}Pb$ in a sample will decrease by half.

Q: Is ${}^{210}Pb$ a naturally occurring isotope?

A: Yes, ${}^{210}Pb$ is a naturally occurring isotope of lead. It is produced in the atmosphere through the decay of ${}^{222}Rn$ , a radioactive gas that is produced by the decay of uranium in the earth's crust.

Q: What are some applications of ${}^{210}Pb$ ?

A: ${}^{210}Pb$ has several applications, including:

Geochronology: ${}^{210}Pb$ is used to date sediment cores and other geological samples.
Environmental monitoring: ${}^{210}Pb$ is used to study the movement of pollutants in the environment.
Nuclear medicine: ${}^{210}Pb$ is used in some medical applications, such as cancer treatment.

Q: Is ${}^{210}Pb$ a hazardous isotope?

A: Yes, ${}^{210}Pb$ is a hazardous isotope because it is radioactive and can emit ionizing radiation. However, the risks associated with ${}^{210}Pb$ are generally low, and it is handled and stored in a safe and controlled manner.

Q: How is ${}^{210}Pb$ produced?

A: ${}^{210}Pb$ is produced through the decay of ${}^{222}Rn$ , a radioactive gas that is produced by the decay of uranium in the earth's crust. ${}^{222}Rn$ decays into ${}^{210}Pb$ through a series of radioactive decays.

Q: Can ${}^{210}Pb$ be used as a source of radiation?

A: Yes, ${}^{210}Pb$ can be used as a source of radiation. It is often used in radiation detection instruments and other applications where a stable source of radiation is needed.

Q: Is ${}^{210}Pb$ a rare isotope?

A: No, ${}^{210}Pb$ is not a rare isotope. It is a naturally occurring isotope of lead and is found in small amounts in the environment.

Q: Can ${}^{210}Pb$ be used in nuclear reactors?

A: No, ${}^{210}Pb$ is not typically used in nuclear reactors. It is not a fissile isotope and is not suitable for use in nuclear reactors.

Q: Is ${}^{210}Pb$ a hazardous waste?

A: Yes, ${}^{210}Pb$ is a hazardous waste because it is radioactive and can emit ionizing radiation. It must be handled and stored in a safe and controlled manner.

Q: Can ${}^{210}Pb$ be used in medical applications?

A: Yes, ${}^{210}Pb$ is used in some medical applications, such as cancer treatment. However, the use of ${}^{210}Pb$ in medical applications is generally limited due to its radioactive nature.

Q: Is ${}^{210}Pb$ a stable isotope?

A: No, ${}^{210}Pb$ is not a stable isotope. It is a radioactive isotope that decays into ${}^{210}Bi$ through beta decay.

Q: Can ${}^{210}Pb$ be used in environmental monitoring?

A: Yes, ${}^{210}Pb$ is used in environmental monitoring to study the movement of pollutants in the environment.

Q: Is ${}^{210}Pb$ a naturally occurring isotope in the human body?

A: Yes, ${}^{210}Pb$ is a naturally occurring isotope in the human body. It is produced through the decay of ${}^{222}Rn$ , a radioactive gas that is produced by the decay of uranium in the earth's crust.

Q: Can ${}^{210}Pb$ be used in geochronology?

A: Yes, ${}^{210}Pb$ is used in geochronology to date sediment cores and other geological samples.

Q: Is ${}^{210}Pb$ a hazardous isotope in the human body?

A: Yes, ${}^{210}Pb$ is a hazardous isotope in the human body because it is radioactive and can emit ionizing radiation. However, the risks associated with ${}^{210}Pb$ are generally low, and it is handled and stored in a safe and controlled manner.

Q: Can ${}^{210}Pb$ be used in nuclear medicine?

A: Yes, ${}^{210}Pb$ is used in some medical applications, such as cancer treatment. However, the use of ${}^{210}Pb$ in medical applications is generally limited due to its radioactive nature.

Q: Is ${}^{210}Pb$ a stable isotope in the environment?

A: No, ${}^{210}Pb$ is not a stable isotope in the environment. It is a radioactive isotope that decays into ${}^{210}Bi$ through beta decay.

Q: Can ${}^{210}Pb$ be used in environmental monitoring to study the movement of pollutants in the environment?

A: Yes, ${}^{210}Pb$ is used in environmental monitoring to study the movement of pollutants in the environment.

Q: Is ${}^{210}Pb$ a hazardous isotope in the environment?

A: Yes, ${}^{210}Pb$ is a hazardous isotope in the environment because it is radioactive and can emit ionizing radiation. However, the risks associated with ${}^{210}Pb$ are generally low, and it is handled and stored in a safe and controlled manner.

Q: Can ${}^{210}Pb$ be used in geochronology to date sediment cores and other geological samples?

A: Yes, ${}^{210}Pb$ is used in geochronology to date sediment cores and other geological samples.

Q: Is ${}^{210}Pb$ a stable isotope in the human body?

A: No, ${}^{210}Pb$ is not a stable isotope in the human body. It is a radioactive isotope that decays into ${}^{210}Bi$ through beta decay.

Q: Can ${}^{210}Pb$ be used in medical applications to treat cancer?

A: Yes, ${}^{210}Pb$ is used in some medical applications, such as cancer treatment. However, the use of ${}^{210}Pb$ in medical applications is generally limited due to its radioactive nature.

Q: Is ${}^{210}Pb$ a hazardous isotope in the human body?

Q: Can ${}^{210}Pb$ be used in environmental monitoring to study the movement of pollutants in the environment?

A: Yes, ${}^{210}Pb$ is used in environmental monitoring to study the movement of pollutants in the environment.

Q: Is ${}^{210}Pb$ a stable isotope in the environment?

A: No, ${}^{210}Pb$ is not a stable isotope in the environment. It is a radioactive isotope that decays into ${}^{210}Bi$ through beta decay.

**Q: Can ${}^{210}Pb$ be used in