Problem 133 - Chemistry A Molecular Approach

Question

Lithium has two naturally occurring isotopes: Li-6 (natural abundance \(7.5 \%\) ) and Li-7 (natural abundance \(92.5 \%\) ). Using circles to represent protons and squares to represent neutrons, draw the nucleus of each isotope. How many Li-6 atoms are present, on average, in a 1000 -atom sample of lithium?

Step-by-Step Solution

Answer

In a 1000-atom sample of lithium, there are, on average, 75 Li-6 atoms.

Step 1: Understanding the Isotopes

Lithium (Li) has two naturally occurring isotopes, Li-6 and Li-7. Li-6 has 3 protons (since it's lithium) and 3 neutrons (since the mass number is 6 - 3 protons = 3 neutrons). Li-7 has 3 protons and 4 neutrons (7 - 3 protons = 4 neutrons).

Step 2: Drawing the Nucleus of Li-6

For Li-6, draw a nucleus with 3 circles to represent the 3 protons and 3 squares to represent the 3 neutrons.

Step 3: Drawing the Nucleus of Li-7

For Li-7, draw a nucleus with 3 circles to represent the 3 protons and 4 squares to represent the 4 neutrons.

Step 4: Calculating the Number of Li-6 Atoms

To find the number of Li-6 atoms in a 1000-atom sample of lithium, multiply the natural abundance of Li-6 (7.5%) by the total number of atoms. Calculation: 1000 atoms * 7.5% = 1000 * 0.075 = 75 Li-6 atoms.

Key Concepts

Atomic Structure

When we talk about the atomic structure, we're looking at the very tiny components that make up an atom. At the center, we have the nucleus, which is composed of protons and neutrons - particles with significant mass. Protons carry a positive electric charge, while neutrons are neutrally charged. Electrons, which are negatively charged and nearly massless compared to protons and neutrons, orbit the nucleus at various energy levels. The atomic number, which is the number of protons in the nucleus, defines the element (like lithium). The mass number, on the other hand, is the total number of protons and neutrons.
Isotopes arise due to the differing numbers of neutrons in the atoms of the same element. As in our example, lithium has isotopes with differing neutron counts, resulting in Li-6 and Li-7; both share the same atomic number but have different mass numbers. It's crucial to understand that the chemical properties of isotopes are very similar, since they have the same number of electrons in similar arrangements, determining their chemistry.

Natural Abundance of Isotopes

Isotopes of an element can have varied natural abundances, determining how often they're found in a naturally occurring sample of the element. This abundance is expressed as a percentage, signifying the fraction of these isotopes you would expect to find. For instance, lithium's two isotopes, Li-6 and Li-7, appear in nature at 7.5% and 92.5% respectively. Therefore, in any batch of lithium atoms, a little over nine-tenths would be Li-7. Understanding this concept is particularly important when working with elements in practical situations, such as in pharmaceuticals, where specific isotopic compositions can affect drug behavior, or in environmental sciences for tracing and dating studies.
When we calculate the number of atoms of a certain isotope in a sample, we use the natural abundance. In our exercise, a 1000-atom sample of lithium contains approximately 75 Li-6 atoms because the natural abundance is 7.5%. This kind of calculation is fundamental in various scientific disciplines, including chemistry, geology, and even in medicine for drug design and diagnostic procedures.

Nucleus Representation

Representing nuclei is key in visualizing and understanding different isotopes. A common method is using simple shapes; circles for protons and squares for neutrons. This representation simplifies complex nuclear compositions, allowing us to easily grasp the differences between isotopes of the same element.
In our original exercise, we've utilized this method to compare the isotopes of lithium. For Li-6, we drew 3 circles for the 3 protons (which define it as lithium), and 3 squares for the 3 neutrons, completing its mass number of 6. Similarly, for Li-7, we've added an extra square to represent the additional neutron. By comparing these drawings, students can intuitively understand that isotopes differ by their number of neutrons. Such visual tools can greatly enhance learning, particularly for visual learners, as they create a simple and memorable image of an otherwise abstract concept.