Problem 9 - Chemistry: Principles and Reactions

Question

How do the isotopes of Cu-63 and Cu-65 differ from each other? Write nuclear symbols for both.

Step-by-Step Solution

Answer

Answer: The nuclear symbols for the isotopes Cu-63 and Cu-65 are \(latex _{29}^{63}\text{Cu}\) and \(latex _{29}^{65}\text{Cu}\), respectively. Cu-63 has 34 neutrons and Cu-65 has 36 neutrons in their nuclei.

Step 1: Understand isotopes

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons in their nuclei. Since they have the same number of protons, they share the same atomic number, but their mass numbers, which are the sum of their protons and neutrons, differ.

Step 2: Determine atomic number and mass numbers

Copper (Cu) has an atomic number of 29, which means there are 29 protons in its nucleus. For its isotopes, Cu-63 and Cu-65, the mass numbers are given as 63 and 65, respectively.

Step 3: Calculate neutrons in each isotope

To find the number of neutrons in each isotope, we subtract the atomic number (29) from their mass numbers: For Cu-63: Number of neutrons = 63 - 29 = 34 For Cu-65: Number of neutrons = 65 - 29 = 36

Step 4: Write nuclear symbols for both isotopes

To write the nuclear symbols for the isotopes, we use the form "Element symbol - Mass number". However, in a more detailed form, we can represent them as: \(latex _{Z}^{A}\text{X}\), where Z is the atomic number, A is the mass number and X is the element symbol. Cu-63: \(latex _{29}^{63}\text{Cu}\) Cu-65: \(latex _{29}^{65}\text{Cu}\)

Key Concepts

Atomic Number

Every element on the periodic table is uniquely identified by its atomic number. The atomic number of an element is the number of protons found in the nucleus of its atoms. Protons are positively charged particles and are one of the primary building blocks of atoms. The atomic number tells us not only the number of protons but also defines the element itself since no two different elements can have the same atomic number. For copper, the atomic number is 29, meaning each atom of copper has 29 protons.
Having the same atomic number ensures elements have similar chemical properties, even if they are isotopes with different mass numbers.

• The atomic number is always a whole number.
• It is denoted as 'Z' in scientific notation.
• It determines the element's position on the periodic table.

No matter how many isotopes an element might have, the atomic number remains unchanged as it is the defining characteristic of the element.

Mass Number

The mass number of an atom is a combination of the total number of protons and neutrons in its nucleus. While the atomic number reflects the chemical properties of an element, the mass number gives us a sense of the atom's mass. Isotopes of an element will have the same atomic number but different mass numbers because they have different numbers of neutrons.
This distinction in mass numbers does not affect the chemical behavior of the element but does impact its nuclear properties.

• The mass number is denoted as 'A'.
• It is not visible on the periodic table and must often be calculated for each isotope.
• For example, in Cu-63, the mass number is 63, meaning a combination of 29 protons and 34 neutrons (as calculated by 63 - 29).

The mass number is crucial for writing nuclear symbols, using the format \(_{Z}^{A}\text{X}\), where 'X' is the chemical symbol, 'Z' is the atomic number, and 'A' is the mass number.

Neutrons in Isotopes

Isotopes are different forms of an element that have the same number of protons (and hence the same atomic number) but different numbers of neutrons. Neutrons are neutral particles that, along with protons, make up an atom's nucleus.To find the number of neutrons in an isotope, subtract the atomic number from the mass number: \( ext{Number of neutrons} = A - Z\).This calculation is straightforward but essential for differentiating between isotopes of the same element.

• Neutrons contribute significantly to the atomic mass but not to the chemical properties.
• The different number of neutrons makes isotopes have different mass numbers.
• For instance,
  • Cu-63 has 34 neutrons (63 - 29).
  • Cu-65 has 36 neutrons (65 - 29).

Understanding neutrons in isotopes helps us grasp why isotopes of the same element can have different physical properties, such as stability or radioactivity, but maintain similar chemical behaviors due to the consistent number of protons.