Rachel Has An Unknown Sample Of A Radioisotope Listed In The Table. Using A Special Technique, She Measures The Mass Of The Unknown Isotope As 104.8 Kg At 12:02:00 P.M. At 4:11:00 P.M. On The Same Day, The Mass Of The Unknown Radioisotope Is 13.1 Kg.

by ADMIN 251 views

Radioactive Decay: Understanding the Half-Life of a Radioisotope

Radioactive decay is a process in which unstable atomic nuclei lose energy through the emission of radiation. This process is characterized by the decay of unstable isotopes into more stable forms, resulting in a decrease in the mass of the original isotope. In this article, we will explore the concept of radioactive decay and how it can be used to determine the half-life of a radioisotope.

Rachel has an unknown sample of a radioisotope listed in the table below.

Isotope Half-Life (years)

Using a special technique, Rachel measures the mass of the unknown isotope as 104.8 kg at 12:02:00 P.M. At 4:11:00 P.M. on the same day, the mass of the unknown radioisotope is 13.1 kg. We are asked to determine the half-life of the radioisotope.

Radioactive decay is a first-order process, meaning that the rate of decay is directly proportional to the amount of the isotope present. This can be expressed mathematically as:

dN/dt = -λN

where N is the amount of the isotope present, λ is the decay constant, and t is time.

The decay constant (λ) is related to the half-life (t1/2) of the isotope by the following equation:

λ = ln(2) / t1/2

where ln(2) is the natural logarithm of 2.

To determine the half-life of the radioisotope, we can use the following equation:

N(t) = N0 * e^(-λt)

where N(t) is the amount of the isotope present at time t, N0 is the initial amount of the isotope, and e is the base of the natural logarithm.

We are given two sets of data: the initial mass of the isotope (104.8 kg) at 12:02:00 P.M. and the mass of the isotope (13.1 kg) at 4:11:00 P.M. on the same day. We can use this data to determine the decay constant (λ) and then the half-life (t1/2) of the isotope.

First, we need to convert the time from hours to years. There are 8760 hours in a non-leap year, so:

12:02:00 P.M. to 4:11:00 P.M. = 4 hours 9 minutes = 4.15 hours

There are 8760 hours in a non-leap year, so:

4.15 hours / 8760 hours/year = 0.0000473 years

Now, we can use the equation above to determine the decay constant (λ):

13.1 kg / 104.8 kg = e^(-λ * 0.0000473 years)

Taking the natural logarithm of both sides, we get:

-0.875 = -λ * 0.0000473 years

Solving for λ, we get:

λ = 18.5 years^-1

Now, we can use the equation above to determine the half-life (t1/2) of the isotope:

t1/2 = ln(2) / λ

Substituting the value of λ, we get:

t1/2 = 0.693 / 18.5 years^-1 = 0.0374 years

Therefore, the half-life of the radioisotope is approximately 0.0374 years.

In this article, we have explored the concept of radioactive decay and how it can be used to determine the half-life of a radioisotope. We have used a special technique to measure the mass of an unknown isotope at two different times and have used this data to determine the decay constant (λ) and then the half-life (t1/2) of the isotope. The half-life of the radioisotope is approximately 0.0374 years.

Radioactive decay is a process in which unstable atomic nuclei lose energy through the emission of radiation. This process is characterized by the decay of unstable isotopes into more stable forms, resulting in a decrease in the mass of the original isotope. In this article, we will answer some frequently asked questions about radioactive decay and its applications.

A: Radioactive decay is a process in which unstable atomic nuclei lose energy through the emission of radiation. This process is characterized by the decay of unstable isotopes into more stable forms, resulting in a decrease in the mass of the original isotope.

A: There are three main types of radioactive decay:

  1. Alpha decay: This type of decay involves the emission of an alpha particle (two protons and two neutrons) from the nucleus of an atom.
  2. Beta decay: This type of decay involves the emission of a beta particle (an electron or a positron) from the nucleus of an atom.
  3. Gamma decay: This type of decay involves the emission of gamma radiation (high-energy photons) from the nucleus of an atom.

A: The half-life of a radioisotope is the time it takes for half of the original amount of the isotope to decay. This is a characteristic property of each radioisotope and is used to determine the rate of decay.

A: The half-life of a radioisotope can be determined by measuring the amount of the isotope present at regular intervals. By plotting a graph of the amount of the isotope against time, the half-life can be calculated.

A: Radioactive decay has many applications in various fields, including:

  1. Medicine: Radioactive isotopes are used in medicine for diagnostic and therapeutic purposes.
  2. Energy production: Radioactive isotopes are used in nuclear power plants to generate electricity.
  3. Scientific research: Radioactive isotopes are used in scientific research to study the properties of materials and the behavior of subatomic particles.
  4. Environmental monitoring: Radioactive isotopes are used to monitor the levels of radioactive materials in the environment.

A: Radioactive decay can pose safety concerns if not handled properly. The radiation emitted by radioactive isotopes can cause harm to humans and the environment. Therefore, it is essential to handle radioactive materials with care and follow proper safety protocols.

A: To protect yourself from radiation, follow these guidelines:

  1. Wear protective clothing: Wear protective clothing, such as gloves and a mask, when handling radioactive materials.
  2. Use shielding: Use shielding materials, such as lead or concrete, to block radiation.
  3. Maintain a safe distance: Maintain a safe distance from radioactive sources.
  4. Follow proper safety protocols: Follow proper safety protocols when handling radioactive materials.

Radioactive decay is a process in which unstable atomic nuclei lose energy through the emission of radiation. This process is characterized by the decay of unstable isotopes into more stable forms, resulting in a decrease in the mass of the original isotope. In this article, we have answered some frequently asked questions about radioactive decay and its applications. By understanding the basics of radioactive decay, we can appreciate its importance in various fields and take necessary precautions to ensure safety.