Question

Each of the following isotopes is used in medicine. Indicate the number of protons and neutrons in each isotope: (a) phosphorus-32, (b) chromium-51, (c) cobalt-60, (d) technetium\(99,(\mathbf{e})\) iodine- \(131,\) (f) thallium-201.

Short answer

(a) Phosphorus-32: 15 protons and 17 neutrons. (b) Chromium-51: 24 protons and 27 neutrons. (c) Cobalt-60: 27 protons and 33 neutrons. (d) Technetium-99: 43 protons and 56 neutrons. (e) Iodine-131: 53 protons and 78 neutrons. (f) Thallium-201: 81 protons and 120 neutrons.

Step-by-step solution

(a) phosphorus-32

Phosphorus (P) has an atomic number (Z) of 15. The isotope has a mass number (A) of 32. The number of neutrons (N) can be found by subtracting the atomic number from the mass number: N = A - Z. N = 32 - 15 = 17 Phosphorus-32 has 15 protons and 17 neutrons.

(b) chromium-51

Chromium (Cr) has an atomic number (Z) of 24. The isotope has a mass number (A) of 51. The number of neutrons (N) can be found by subtracting the atomic number from the mass number: N = A - Z. N = 51 - 24 = 27 Chromium-51 has 24 protons and 27 neutrons.

(c) cobalt-60

Cobalt (Co) has an atomic number (Z) of 27. The isotope has a mass number (A) of 60. The number of neutrons (N) can be found by subtracting the atomic number from the mass number: N = A - Z. N = 60 - 27 = 33 Cobalt-60 has 27 protons and 33 neutrons.

(d) technetium-99

Technetium (Tc) has an atomic number (Z) of 43. The isotope has a mass number (A) of 99. The number of neutrons (N) can be found by subtracting the atomic number from the mass number: N = A - Z. N = 99 - 43 = 56 Technetium-99 has 43 protons and 56 neutrons.

(e) iodine-131

Iodine (I) has an atomic number (Z) of 53. The isotope has a mass number (A) of 131. The number of neutrons (N) can be found by subtracting the atomic number from the mass number: N = A - Z. N = 131 - 53 = 78 Iodine-131 has 53 protons and 78 neutrons.

(f) thallium-201

Thallium (Tl) has an atomic number (Z) of 81. The isotope has a mass number (A) of 201. The number of neutrons (N) can be found by subtracting the atomic number from the mass number: N = A - Z. N = 201 - 81 = 120 Thallium-201 has 81 protons and 120 neutrons.

Key concepts

Atomic Number

The atomic number, represented by the symbol 'Z', is a fundamental property of an element. It indicates the number of protons in the nucleus of an atom. Protons are positively charged particles, and their number defines the element itself—for instance, hydrogen has an atomic number of 1, meaning it has one proton, while carbon has an atomic number of 6.

Protons also determine the chemical behavior of an atom because they interact with electrons—negatively charged particles that orbit the atom's nucleus. The electrons are arranged in layers or shells, and their arrangement is governed by the number of protons. Elements with the same atomic number share the same chemical properties and are categorized as the same element, but they may have different mass numbers due to variations in their neutrons, resulting in different isotopes.

Mass Number

The mass number, denoted by 'A', is the total number of protons and neutrons in an atom's nucleus. Neutrons, like protons, are particles located in the nucleus, but they carry no electrical charge. They add to the mass of an atom but not to its charge.

The mass number is critical for isotopes, which are atoms of the same element (same number of protons) with different numbers of neutrons. For example, carbon-12, the most common isotope of carbon, has 6 protons and 6 neutrons. Carbon-14, on the other hand, has 6 protons like carbon-12, but it has 8 neutrons. It's this variation in the neutron number that gives isotopes their unique properties, and the mass number is a convenient way to express the total number of these nucleons.

Neutron Calculation

To calculate the number of neutrons in an isotope, you subtract the atomic number from the mass number: Neutron number (N) = Mass number (A) - Atomic number (Z).For instance, in phosphorus-32, with an atomic number of 15 and a mass number of 32, the number of neutrons is calculated by subtracting 15 from 32, giving you 17 neutrons. This simple computation helps you understand the internal structure of an atom, which is crucial when studying isotopes used in medicine. A correct neutron count is essential for comprehending behaviors and properties such as radioactive decay, which is a principle applied in medical diagnostics and treatment.

Medical Isotopes

Medical isotopes are variants of elements used in healthcare, primarily for diagnostic imaging and cancer treatment. For example, Technetium-99m, where 'm' stands for metastable, is widely used in radiography to image the skeleton and heart muscle. It is preferred due to its ideal half-life and the type of radiation it emits.

Another isotope, Iodine-131, is used to treat thyroid cancer and diagnose thyroid disorders. Its radioactive decay allows it to be detected in the body with appropriate imaging techniques and also helps to destroy diseased cells. Medical isotopes exemplify the practical application of nuclear physics in improving health outcomes.

Understanding atomic and mass numbers is not just academic; it's the backbone of utilizing medical isotopes safely and effectively. This knowledge aids professionals in choosing the appropriate isotope with the suitable properties—like half-life and type of decay—for various medical procedures.