Problem 114 - Chemistry Matter and Change

Question

An atom of gadolinium has an atomic number of 64 and a mass number of \(153 .\) How many electrons, protons, and neutrons does it contain? (Chapter 4\()\)

Step-by-Step Solution

Answer

Gadolinium has 64 protons, 64 electrons, and 89 neutrons.

Step 1: Determine the number of protons

The atomic number of an element is equal to the number of protons in its nucleus. Gadolinium has an atomic number of 64, which means it has 64 protons.

Step 2: Determine the number of electrons

In a neutral atom, the number of electrons is equal to the number of protons. Therefore, gadolinium also has 64 electrons.

Step 3: Calculate the number of neutrons

The mass number is the sum of the number of protons and neutrons in an atom. For gadolinium, the mass number is 153. This can be expressed as the equation: \[ \text{Mass Number} = \text{Number of Protons} + \text{Number of Neutrons} \]Plug in the values:\[ 153 = 64 + \text{Number of Neutrons} \]To find the number of neutrons, subtract the atomic number (number of protons) from the mass number:\[ \text{Number of Neutrons} = 153 - 64 = 89 \]

Key Concepts

Understanding Atomic Number

The atomic number is a fundamental property of an atom and holds significant importance in the field of chemistry. It defines the identity of an element and is denoted by the symbol 'Z'. The atomic number represents the number of protons found in the nucleus of an atom. Each element on the periodic table has a unique atomic number, which tells us not just about the protons but indirectly about electrons in a neutral atom.

- **Key Points about Atomic Number:** - It uniquely identifies each element. - The number of protons equals the atomic number. - For a neutral atom, the atomic number also equals the number of electrons.
In the case of gadolinium, its atomic number is 64, meaning it has 64 protons. This unique atomic number places gadolinium in the lanthanide series within the periodic table, giving it specific chemical properties that differ from other elements. Without understanding the atomic number, the landscape of chemistry and the periodic table would lack structure and order.

Exploring Mass Number

The mass number is another critical aspect of an atom's structure and is represented by the letter 'A'. It provides the total count of protons and neutrons in an atom's nucleus. Unlike the atomic number, which is fixed for each element, the mass number can vary due to the presence of isotopes. Isotopes are different forms of the same element with a different number of neutrons.

- **Key Points about Mass Number:** - It's the sum of protons and neutrons in the nucleus. - Isotopes of the same element have different mass numbers. - Mass number is not found directly on the periodic table but can be calculated if neutrons and protons are known.
For gadolinium's mass number of 153, we deduce there are 153 protons and neutrons combined. Knowing that it has 64 protons (from its atomic number), we calculate the neutrons in gadolinium by subtracting the number of protons from the mass number:\[ \text{Number of Neutrons} = 153 - 64 = 89 \]Understanding the mass number is crucial for grasping atomic stability and the nature of isotopes.

Gadolinium: A Special Element

Gadolinium is one of the intriguing elements found in the periodic table, with its distinct properties that make it valuable in various applications. With an atomic number of 64 and falling under the lanthanides category, it's notable for its magnetic properties and its ability to absorb neutrons, which makes it useful in medical and industrial fields.

- **Key Characteristics of Gadolinium:** - Belongs to the lanthanide series. - Atomic number of 64. - Mass number often around 153. - Strong magnetic properties. - High neutron absorption capability.
Connected to these properties are gadolinium's uses in MRI contrast agents and in nuclear reactors. In medical imaging, it enhances the contrast between tissues, providing clear images for better diagnosis. In nuclear technology, it acts as a safety feature for its capability to capture free neutrons, thus preventing unwanted reactions. Recognizing these characteristics and uses of gadolinium highlights the connection between its atomic structure and practical applications.