Problem 8 - Chemistry for Allied Health

Question

How many protons, neutrons, and electrons are there in an atom of lead-207?

Step-by-Step Solution

Answer

Lead-207 has 82 protons, 125 neutrons, and 82 electrons.

Step 1: Identify the Atomic Number

The atomic number of lead (Pb) is 82. This indicates there are 82 protons in a lead atom and, in a neutral atom, 82 electrons as well because the number of protons equals the number of electrons.

Step 2: Calculate the Neutron Count

The atomic mass of lead in this isotope, lead-207, is 207. To find the number of neutrons, subtract the atomic number (number of protons) from the atomic mass: \(207 - 82 = 125\). This means there are 125 neutrons in an atom of lead-207.

Step 3: Verify the Electron Count

In a neutral atom like lead-207, the number of electrons must equal the number of protons to balance the charge. Therefore, there are 82 electrons in a lead-207 atom.

Key Concepts

Atomic Number

The atomic number is a fundamental concept in understanding atomic structure. It is the number of protons found in the nucleus of an atom. Essentially, the atomic number defines an element. For instance, lead has an atomic number of 82, which means every atom of lead contains 82 protons. This number is unique to lead and is used as an identifying characteristic.

• Determines the element's identity and properties.
• Equals the number of protons.
• For neutral atoms, it also equals the number of electrons.

This correspondence between protons and electrons is crucial, as it ensures that an atom is electrically neutral. Without an equal number of these subatomic particles, the atom would carry an electric charge, turning it into an ion.

Neutrons

Neutrons are subatomic particles found in the nucleus of an atom, alongside protons. They are neutral, carrying no electrical charge. To determine the number of neutrons in an atom, one must know both the atomic mass and the atomic number. The atomic mass is the total number of protons and neutrons.
The formula to find neutrons is:
\[\text{Number of neutrons} = \text{Atomic mass} - \text{Atomic number}\]In the case of lead-207, the atomic mass is 207, and the atomic number is 82. Therefore:
\[207 - 82 = 125\]

• Neutrons contribute to the atomic mass.
• They help stabilize the nucleus by offsetting repulsive forces between protons.

Without an appropriate number of neutrons, the nucleus could become unstable and susceptible to radioactive decay.

Protons

Protons are positively charged particles located in the nucleus of an atom. They, along with neutrons, make up almost all of an atom's mass. The number of protons in an atom determines the element's identity and is equal to the atomic number.
For example, lead, with an atomic number of 82, contains 82 protons. This is a constant characteristic for each element:

• Defines the chemical element.
• Positively charged, balancing the negative charge of electrons.
• Protons and neutrons together are often referred to as nucleons.

Protons play a vital role in binding the atomic nucleus together, interacting with neutrons to maintain the nucleus's integrity. They also influence many of the atom's chemical properties.

Isotopes

Isotopes are variants of a particular chemical element that share the same number of protons but differ in the number of neutrons. This variation in neutron number means isotopes have different atomic masses but share similar chemical properties.
Lead-207 is an isotope of lead. While all lead atoms have 82 protons, lead-207 contains 125 neutrons, differing from other isotopes of lead:

• Isotopes have identical atomic numbers but different atomic mass.
• They exhibit similar chemical behavior.
• Isotopes can be stable or radioactive.

Understanding isotopes is essential in fields like radiographic dating, nuclear medicine, and atom research, where isotopes' unique properties are utilized for various applications.