Problem 5 - College Physics

Question

One isotope of uranium has a mass number of 235 , and another has a mass number of \(238 .\) What are the numbers of protons, neutrons, and electrons in a neutral atom of each isotope?

Step-by-Step Solution

Answer

Uranium-235: 92 protons, 143 neutrons, 92 electrons; Uranium-238: 92 protons, 146 neutrons, 92 electrons.

Step 1: Understanding Isotopes

Isotopes of an element are atoms with the same number of protons but different numbers of neutrons. Uranium, like any neutral atom, has an equal number of electrons and protons.

Step 2: Determining Protons and Electrons

Uranium's atomic number is 92, meaning every uranium atom, including isotopes, has 92 protons. In a neutral atom, this also means it has 92 electrons.

Step 3: Calculating Neutrons for Uranium-235

The mass number of an isotope (uranium-235 in this case) is the sum of protons and neutrons: \[\text{Number of neutrons} = \text{Mass number} - \text{Number of protons} = 235 - 92 = 143.\]

Step 4: Calculating Neutrons for Uranium-238

Similarly, for uranium-238:\[\text{Number of neutrons} = \text{Mass number} - \text{Number of protons} = 238 - 92 = 146.\]

Step 5: Summarizing Results

For uranium-235: 92 protons, 143 neutrons, 92 electrons. For uranium-238: 92 protons, 146 neutrons, 92 electrons.

Key Concepts

Uranium

Uranium is a heavy metal that is commonly used as fuel in nuclear reactors. It is symbolized by "U" and is well known for being radioactive. Uranium's atomic number is 92, which means every atom of uranium has 92 protons in its nucleus. This atomic number is identical across all uranium isotopes, but the number of neutrons can change.
Uranium has several isotopes, with uranium-235 and uranium-238 being the most prevalent. Despite the difference in neutrons, these isotopes exhibit similar chemical behavior because their electron configurations are the same, owing to having the same number of protons.
In terms of natural abundance, uranium-238 is more prevalent than uranium-235. The distinct property of uranium-235 is its ability to sustain a nuclear chain reaction, which is why it is commonly used for nuclear power and in atomic bombs.

Atomic Structure

The atomic structure describes how an atom is organized. At the center of an atom, there is a nucleus which contains protons and neutrons. Surrounding the nucleus, in various energy levels or shells, are electrons. Electrons are much smaller compared to protons and neutrons.
The number of protons determines the element's identity. For instance, any atom with 92 protons is recognized as uranium. Every proton carries a positive charge. Neutrons are neutral, meaning they have no charge. Electrons are negatively charged and balance the positive charge of protons in a neutral atom.

• Protons and neutrons are tightly bound in the central nucleus, giving the atom most of its mass.
• Electrons orbit the nucleus, influencing the chemical properties and bonding behavior of the atom.

Understanding atomic structure is fundamental for explaining an element's behavior, including bonding and interaction with other elements.

Neutrons

Neutrons are essential components of an atom's nucleus. They are similar in mass to protons but do not carry an electrical charge, which is why they are called 'neutral'.
In uranium, neutrons contribute significantly to the mass of the atom and play a crucial role in the stability of the nucleus. Changes in the number of neutrons result in different isotopes of uranium. For example:

• Uranium-235 has 143 neutrons.
• Uranium-238 has 146 neutrons.

These extra neutrons in uranium-238 make it heavier and contribute to its longer half-life compared to uranium-235. Neutrons also affect the radioactive properties of uranium, making it useful for various applications in energy and medicine.

Protons

Protons are positively charged particles found in the nucleus of an atom. In uranium, there are always 92 protons as this defines the element and gives it its atomic number.
Protons significantly impact the overall charge and stability of the atom. Since they carry a positive charge, they attract the negatively charged electrons, which orbit the nucleus. This interaction between protons and electrons keeps the atom together and stable. The number of protons in an atom is critical because it determines not only the chemical element but also its place in the periodic table and various chemical properties.

• Changing the number of protons in the nucleus transforms the element into a completely different one.
• The number of protons equals the number of electrons in a neutral atom, balancing the electrical charge.

Hence, understanding protons is key to understanding atomic identity and behavior.

Electrons

Electrons are tiny, negatively charged particles that orbit the nucleus of an atom. Despite their small size, they are critical in determining how atoms interact with each other.
In a neutral uranium atom, there are 92 electrons, matching the number of protons. These electrons exist in various energy levels or shells around the nucleus. Their arrangement or configuration affects the atom's chemical properties and how it participates in chemical bonds.
Because the number of electrons in a neutral atom equals the number of protons, the positive and negative charges cancel each other out, resulting in no overall charge for the atom. Electrons can move between energy levels when the atom absorbs or releases energy, a process integral to chemical reactions and bonds.

• Electrons in the outermost shell, known as valence electrons, play a crucial role in chemical bonding.
• The interaction of electrons with light and energy forms the basis of much of chemistry and physics.

Understanding electrons and their behavior leads to deeper insights into chemical reactions and properties.