Problem 28 - Chemistry: The Central Science

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, (e) iodine-131, (f) thallium-201.

Step-by-Step Solution

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 1: Determine the atomic numbers

We will find the atomic number of each element which represents the number of protons: - Phosphorus (P) has an atomic number of 15. - Chromium (Cr) has an atomic number of 24. - Cobalt (Co) has an atomic number of 27. - Technetium (Tc) has an atomic number of 43. - Iodine (I) has an atomic number of 53. - Thallium (Tl) has an atomic number of 81.

Step 2: Calculate the number of neutrons

We'll subtract the atomic number of each element from its given mass number to find the number of neutrons: (a) For phosphorus-32: \( 32 - 15 = 17 \) neutrons (b) For chromium-51: \( 51 - 24 = 27 \) neutrons (c) For cobalt-60: \( 60 - 27 = 33 \) neutrons (d) For technetium-99: \( 99 - 43 = 56 \) neutrons (e) For iodine-131: \( 131 - 53 = 78 \) neutrons (f) For thallium-201: \( 201 - 81 = 120 \) neutrons

Step 3: Summary of the results

We have found the number of protons and neutrons for each isotope: (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

Key Concepts

Atomic Number

Atoms are made up of three main subatomic particles: protons, neutrons, and electrons. The atomic number of an element is a crucial identifier and tells us the number of protons present in an atom's nucleus. Since protons carry a positive charge, the atomic number also indirectly informs us about the positive charge within the nucleus. Besides, in a neutral atom, the number of electrons equals the number of protons. This means the atomic number not only specifies the number of protons but also the number of electrons.

• The atomic number is unique for each element. For example, carbon has an atomic number of 6, meaning every carbon atom has 6 protons.
• In isotopes, the atomic number remains the same across different forms of the element because the number of protons doesn’t change.

Knowing the atomic number is essential because it helps distinguish one element from another in the vast periodic table of elements.

Mass Number

The mass number represents the total number of protons and neutrons in an atom's nucleus, making it crucial for understanding isotopes. Unlike the atomic number, which is always the same for a given element, the mass number can differ even among atoms of the same element. Isotopes are atoms with the same number of protons (and hence the same atomic number) but different numbers of neutrons. This variance leads to different mass numbers for each isotope of an element, like iodine-131 and iodine-127, which are common isotopes used in medical applications.

• To find the mass number, simply add the number of protons and neutrons together.
• While the atomic number identifies the element, the mass number gives insights into the particular isotope of the element by indicating the total mass of the nucleus.

Understanding mass number helps scientists identify specific isotopes, which can be pivotal in fields like nuclear medicine, where stability and decay rates of isotopes are important.

Neutrons

Neutrons are neutral subatomic particles found in the nucleus of an atom. They play a critical role in the stability of the atom's nucleus. Neutrons, along with protons, contribute to the atomic mass but do not affect the chemical identity of the element. The number of neutrons can vary within atoms of the same element, leading to isotopes. To calculate the number of neutrons in an atom, subtract the atomic number from the mass number: \[ \text{Number of neutrons} = \text{Mass number} - \text{Atomic number} \]

• An example is carbon-12 and carbon-14; both have 6 protons, but their neutron numbers differ, leading to different isotopes.
• Neutrons are crucial for nuclear reactions and stability; too many or too few can lead to radioactivity.

By understanding the number of neutrons, scientists can better understand the properties and behavior of isotopes, which can influence their applications in different scientific fields.

Protons

Protons are positively charged particles found within the nucleus of an atom. They're fundamental components of atomic structure. Each proton has a relative charge of +1, contributing significantly to the atom's characteristics and behavior. The number of protons determines the atomic number of an element, and fundamentally, its position in the periodic table. This means the number of protons is identical across all atoms of a particular element.

• Protons play a key role in chemical reactions by interacting with electrons. For example, hydrogen, with one proton, is highly reactive.
• Changing the number of protons in an atom transforms it into a different element, highlighting the significance of protons in atomic identity.

Understanding protons and their role is vital for grasping concepts in chemistry and physics, as they help define the fundamental nature of matter throughout the universe.