Problem 81 - General Chemistry: Principles and Modern Applications

Question

One of the following elements has eight naturally occurring stable isotopes. We should expect that one to be (a) \(\mathrm{Ra} ;\) (b) \(\mathrm{Au} ;\) (c) \(\mathrm{Cd} ;\) (d) Br.

Step-by-Step Solution

Answer

The element among Ra, Au, Cd, and Br that has eight naturally occurring stable isotopes is Cadmium (Cd).

Step 1: Identify the number of stable isotopes for Radium (Ra)

Radium (Ra) has no naturally occurring stable isotopes. All its isotopes are radioactive, meaning they decay over time releasing radiation.

Step 2: Identify the number of stable isotopes for Gold (Au)

Gold (Au) has only one stable isotope, which is \( \text{Au-197} \).

Step 3: Identify the number of stable isotopes for Cadmium (Cd)

Cadmium (Cd) has eight naturally occurring stable isotopes: Cd-106, Cd-108, Cd-110, Cd-111, Cd-112, Cd-113, Cd-114, and Cd-116.

Step 4: Identify the number of stable isotopes for Bromine (Br)

Bromine (Br) has two naturally occurring isotopes, Br-79 and Br-81.

Key Concepts

Element Isotopes

Isotopes are like twins of an element; they have the same number of protons but different numbers of neutrons. This means isotopes of a single element have the same atomic number but different atomic masses. For any given element, isotopes may either be stable or unstable (radioactive).

• Stable isotopes remain constant over time as they do not undergo radioactive decay.
• Unstable isotopes, however, will change over time through radioactive decay.

Cadmium serves as a fascinating example with eight stable isotopes like Cd-106, Cd-108, and Cd-110. Despite having different nuclear masses, each of these isotopes retains the chemical properties of Cadmium. This is due to their consistent proton count of 48.

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. It is a natural and spontaneous process that results in the transformation of one element into another.

• During decay, isotopes emit particles and energy in the form of alpha particles, beta particles, or gamma rays.
• The time it takes for half of a sample of radioactive material to decay is known as its 'half-life'.

For example, all isotopes of Radium are radioactive. This means they are unstable and undergo radioactive decay, leading to the emission of radiation over time. The absence of stable isotopes for Radium is a characteristic that makes it distinct from elements like Gold, which has one stable isotope, and Cadmium, with its eight stable isotopes.

Naturally Occurring Isotopes

Naturally occurring isotopes are those that can be found in nature without human intervention. These are either stable or have an extremely long half-life, allowing them to exist naturally over long periods. Elements can have several isotopes, but not all of them need to be stable.

• Gold, for instance, naturally occurs with only one stable isotope, Au-197.
• Bromine occurs naturally with two isotopes, Br-79 and Br-81.

Natural isotopes play a crucial role in the environment and are fundamental in processes across geology, biology, and chemistry. They are essential in scientific applications such as radiometric dating and tracing chemical pathways in ecosystems.