Question

The atomic number of silver, \(\mathrm{Ag}\), is 47 and it has an average atomic mass of 107.87 . Why is it impossible to determine the number of neutrons in the nucleus of a silver atom?

Short answer

The number of neutrons in a silver atom cannot be determined just by its atomic number (47) and average atomic mass (107.87), because the average atomic mass is a weighted average that includes all isotopes of silver, which have varying numbers of neutrons.

Step-by-step solution

Understanding Atomic Number

The atomic number of an element, in this case silver (Ag), represents the number of protons in the nucleus of the atom. For silver, the atomic number is 47, which means there are 47 protons in its nucleus.

Understanding Average Atomic Mass

The average atomic mass of an element is the weighted average of the masses of the isotopes of that element. It takes into account the masses of all the isotopes and their relative abundance. The average atomic mass for silver is given as 107.87.

Why Neutron Number Cannot Be Determined Directly

Knowing the average atomic mass and the atomic number alone does not provide enough information to determine the exact number of neutrons in a silver atom. This is because the average atomic mass represents an average over all the isotopes of silver, and these isotopes can have different numbers of neutrons. Thus, without knowing the specific isotope of silver, you cannot precisely determine the number of neutrons.

Key concepts

Average Atomic Mass

The concept of average atomic mass is foundational in understanding elements and their isotopes. Every element on the periodic table, such as silver (Ag), is made up of atoms with a specific number of protons in their nucleus, which defines the element's atomic number. However, atomic mass is a different story. Let's look at silver, which has an average atomic mass of 107.87.

The term 'average atomic mass' refers to the weighted average of the atomic masses of all the naturally occurring isotopes of an element. This means it takes the mass of each isotope and multiplies it by the percentage of its natural abundance. These values are then summed to give the average mass. For example, imagine there are two silver isotopes: one that is heavier and less abundant, and one that is lighter but more common. The average atomic mass factors in both the heavier isotope's greater mass and the lighter isotope's higher occurrence, resulting in the average of 107.87.

Why is this average so important? It's because when dealing with large amounts of an element, you're not dealing with just one atom and one mass. You're dealing with a mix, and that's what average atomic mass represents - the mix of isotopes you'd expect to find in a naturally occurring sample of that element.

Isotopes

Diving into the world of isotopes can be incredibly interesting. Isotopes are different forms of the same element that have the same number of protons but a different number of neutrons in their nuclei. This variance in neutron number leads to differences in atomic mass. For instance, silver (Ag) has an atomic number of 47, meaning each silver atom has 47 protons. However, silver isotopes differ in the number of neutrons they possess.

These isotopic differences are natural. In the universe, it's common for elements to have multiple stable forms. For silver, most of it exists as two main isotopes: Silver-107 and Silver-109. They are chemically identical, but Silver-109 has two more neutrons than Silver-107. These isotopes each have their unique atomic masses and occur in nature in a certain ratio, which is crucial when calculating the average atomic mass of an element.

Studying isotopes is essential not only for understanding chemical reactions but also in various applications such as radiometric dating, medical diagnostics, and tracing chemical pathways in the environment. Scientists make use of these slight mass differences for a range of scientific and technological applications.

Neutrons in the Nucleus

Neutrons are the somewhat mysterious sibling to the proton. Residing in the nucleus of an atom alongside protons, neutrons play a critical role in providing stability and mass to atoms. The number of neutrons can vary even among atoms of the same element, which is the basis for the existence of isotopes.

Unlike protons, neutrons do not have an electrical charge, and hence, they are neutrally charged particles. Their primary job is to add mass to the atom and help to hold the nucleus together through the strong nuclear force, overcoming the repulsive forces between the positively charged protons.

For silver, with its atomic number of 47, each atom has 47 protons. The number of neutrons, however, is not fixed and can differ depending on the isotope. Since the atomic mass is essentially the sum of the protons and neutrons (electrons contribute negligibly), knowing the number of protons does not give us a direct count of neutrons. This is why from the average atomic mass and atomic number alone, we cannot pinpoint the exact number of neutrons in an atom without specific isotope information. This variability is what makes nature both beautiful and complex, as the different configurations of neutrons give rise to the diversity of isotopic forms in the elements.