Question

Copper (Cu) consists of two naturally occurring isotopes with masses of 62.9296 and 64.9278 u. (a) How many protons and neutrons are in the nucleus of each isotope? Write the complete atomic symbol for each, showing the atomic number and mass number. (b) The average atomic mass of Cu is $63.55\mathrm{u}$. Calculate the abundance of each isotope.

Short answer

The two naturally occurring isotopes of Copper, ${}_{29}^{63}\text{Cu}$ and ${}_{29}^{65}\text{Cu}$, have 29 protons and 34 or 36 neutrons in their nucleus, respectively. The abundance of each isotope is 69.18% for ${}_{29}^{63}\text{Cu}$ and 30.82% for ${}_{29}^{65}\text{Cu}$.

Step-by-step solution

Find the atomic number of Copper (Cu)

Copper is a chemical element, and its atomic number can be found in the periodic table. In the periodic table, Copper is represented by the symbol Cu and has an atomic number of 29.

Determine the number of protons and neutrons in each isotope

Since the atomic number of Copper is 29, it means that Copper has 29 protons in its nucleus. For the first isotope with mass 62.9296 u, the number of neutrons can be found as follows: Number of neutrons = mass number - atomic number = 63 (rounded) - 29 = 34 neutrons For the second isotope with mass 64.9278 u, the number of neutrons can be found as follows: Number of neutrons = mass number - atomic number = 65 (rounded) - 29 = 36 neutrons

Write the complete atomic symbol for each isotope

The complete atomic symbol for each isotope can be written as: Isotope 1: ${}_{29}^{63}\text{Cu}$ (29 protons and 34 neutrons) Isotope 2: ${}_{29}^{65}\text{Cu}$ (29 protons and 36 neutrons)

Calculate the abundance of each isotope using the average atomic mass

Let x be the abundance of isotope 1 (${}_{29}^{63}\text{Cu}$) and (1-x) be the abundance of isotope 2 (${}_{29}^{65}\text{Cu}$). The sum of the product of each isotope mass and its abundance should equal the average atomic mass of Copper, which is given as 63.55 u. 62.9296 * x + 64.9278 * (1-x) = 63.55 Now, we solve for x: x = (63.55 - 64.9278) / (62.9296 - 64.9278) = 0.6918 Thus, the abundance of isotope 1 (${}_{29}^{63}\text{Cu}$) is 69.18%, and the abundance of isotope 2 (${}_{29}^{65}\text{Cu}$) is 100 - 69.18 = 30.82%.

Key concepts

Atomic Number

In chemistry, understanding the atomic number of an element is fundamental. The atomic number of an element, like Copper, is crucial because it indicates the number of protons in the nucleus of an atom. The atomic number is essentially the identity of an element on the periodic table. For instance, Copper is represented by the letter "Cu" and has an atomic number of 29. This means that every atom of Copper has 29 protons. This atomic number not only tells us the number of protons but also defines the element itself, as changing the number of protons transforms one element into another. The atomic number also plays a key role in determining how elements interact with each other. Therefore, knowing the atomic number helps scientists predict the types of chemical bonds an element can form.

Protons and Neutrons

Protons and neutrons make up the nucleus of an atom and are often referred to as nucleons. Their presence and number essentially define the specific isotopes of an element. In every element, the number of protons is equal to the atomic number, which for Copper is 29, meaning each Copper atom has 29 protons. Neutrons, on the other hand, vary among isotopes. For Copper, isotopes can have different numbers of neutrons. For example, copper's two naturally occurring isotopes have mass numbers of approximately 63 and 65. Calculating the number of neutrons involves subtracting the atomic number from the mass number:- For the isotope ${}_{29}^{63}\text{Cu}$: 63 - 29 = 34 \text{ neutrons}\- For the isotope ${}_{29}^{65}\text{Cu}$: 65 - 29 = 36 \text{ neutrons}\The variety in neutron count among isotopes gives rise to different atomic masses, which we see in the form of isotopic masses.

Atomic Symbol

Each element is represented by an atomic symbol, a concise way to convey key information about an atom. The atomic symbol consists of the element's letter symbol, usually derived from its English or Latin name, alongside its atomic number and mass number. For Copper, the symbol is ${}_{29}^{63}\text{Cu}$ or ${}_{29}^{65}\text{Cu}$, dependent on the isotope. The lower number (subscript) in the symbol represents the atomic number, showing the number of protons. Meanwhile, the upper number (superscript) shows the mass number, which is the sum of protons and neutrons in the nucleus. This format is particularly useful as it provides a clear visual representation of the element's properties and isotopic composition. Such precise notations are essential in chemistry for distinguishing between similar elements and isotopes.

Average Atomic Mass

The average atomic mass is a weighted average of the masses of an element's naturally occurring isotopes. Unlike a simple arithmetic mean, this average takes into account the relative abundance of each isotope. For Copper, which has isotopes approximated at 63 and 65 mass units, the average atomic mass is given as 63.55 u. To find this average, we calculate: - Multiply the mass of each isotope by its relative abundance. - Add these values together. This calculation helps predict which isotopes are more prevalent in nature and gives a universal atomic mass for use in chemical equations. As isotopes have different masses, they contribute differently to the overall atomic mass of an element. Understanding average atomic mass helps in various applications, such as material science, chemical manufacturing, and nuclear physics.