Naturally occurring cobalt consists of only one isotope, 59Co, whose relative atomic mass is 58.9332. A synthetic radioactive isotope of cobalt, 60Co, relative atomic mass 59.9338, is used in radiation therapy for cancer. A 1.5886-g sample of cobalt has an apparent 'atomic mass' of 58.9901. Find the mass of 60Co in this sample.

Radioactive isotopes, also known as radioisotopes, are variants of chemical elements that have an unstable combination of neutrons and protons in their atomic nuclei. This instability causes them to lose energy in the form of radiation, which can be alpha, beta, or gamma rays.

For instance, the element cobalt has two isotopes of interest: stable 59Co and radioactive 60Co. The latter is synthetic and undergoes decay, emitting beta particles and gamma radiation. This property makes it useful in applications such as medical treatment and industrial radiography.

The behavior of radioactive isotopes is governed by principles of nuclear physics rather than the chemical properties of the elements. When working with radioisotopes, safety is paramount due to the potential health risks associated with radiation exposure.

The concept of weighted average atomic mass plays a crucial role in understanding how the apparent atomic mass of a sample containing multiple isotopes is calculated. The weighted average takes into consideration the relative abundance and the atomic mass of each isotope present.

To calculate a weighted average atomic mass, one multiplies the mass of each isotope by its relative proportion in the sample and then sums these values. In the case of the cobalt sample from the exercise, the measured atomic mass is a weighted average based on the mass and relative abundance of the isotopes 59Co and 60Co in the sample.

Knowing how to calculate the weighted average atomic mass provides insight into the composition of elements and their isotopes naturally occurring or present in a given sample, as demonstrated in the tutorial exercise where this concept was applied to find the mass of 60Co.

Radiation therapy for cancer utilizes high-energy radiation to kill cancer cells or impede their growth. This treatment leverages radioactive isotopes, like 60Co, to deliver targeted radiation. As the isotopes decay, they emit radiation that can damage the DNA of malignant cells, leading to cancer cell death or the inhibition of replication.

Radiation therapy can be administered externally, where a machine outside the body directs radiation towards the cancer, or internally, through brachytherapy, where radioactive sources are placed inside the body. The effectiveness and precision of radiation therapy have been significantly improved due to advancements in medical technology, helping to minimize damage to surrounding healthy tissues.

Understanding the properties of radioactive isotopes and their applications in treatments like radiation therapy is not only crucial for students in the sciences but is also valuable knowledge for anyone interested in modern medical practices.