Problem 46 - Chemistry An Atoms First Approach

Question

Write the atomic symbol \(\left(\frac{1}{2} X\right)\) for each of the isotopes described below. a. number of protons \(=27,\) number of neutrons \(=31\) b. the isotope of boron with mass number 10 c. \(Z=12, A=23\) d. atomic number \(53,\) number of neutrons \(=79\) e. \(Z=20,\) number of neutrons \(=27\) f. number of protons \(=29,\) mass number 65

Step-by-Step Solution

Answer

The atomic symbols for the given isotopes are as follows: a. \(\left(_{27}^{58}\textrm{Co}\right)\) b. \(\left(_{5}^{10}\textrm{B}\right)\) c. \(\left(_{12}^{23}\textrm{Mg}\right)\) d. \(\left(_{53}^{132}\textrm{I}\right)\) e. \(\left(_{20}^{47}\textrm{Ca}\right)\) f. \(\left(_{29}^{65}\textrm{Cu}\right)\)

Step 1: a. Isotope with 27 protons and 31 neutrons

Step 1: \(Z = 27\) Step 2: \(A = Z + \textrm{neutrons} = 27 + 31 = 58\) Step 3: \(X = \textrm{Cobalt (Co)}\) (Element with 27 protons) The atomic symbol for this isotope is \(\left(_{27}^{58}\textrm{Co}\right)\).

Step 2: b. Isotope of boron with mass number 10

Step 1: \(Z = 5\) (Boron has 5 protons) Step 2: \(A = 10\) Step 3: \(X = \textrm{Boron (B)}\) The atomic symbol for this isotope is \(\left(_{5}^{10}\textrm{B}\right)\).

Step 3: c. Isotope with Z=12 and A=23

Step 1: \(Z = 12\) Step 2: \(A = 23 \) Step 3: \(X = \textrm{Magnesium (Mg)}\) (Element with 12 protons) The atomic symbol for this isotope is \(\left(_{12}^{23}\textrm{Mg}\right)\).

Step 4: d. Isotope with atomic number 53 and 79 neutrons

Step 1: \(Z = 53\) Step 2: \(A = Z + \textrm{neutrons} = 53 + 79 = 132\) Step 3: \(X = \textrm{Iodine (I)}\) (Element with 53 protons) The atomic symbol for this isotope is \(\left(_{53}^{132}\textrm{I}\right)\).

Step 5: e. Isotope with Z=20 and 27 neutrons

Step 1: \(Z = 20\) Step 2: \(A = Z + \textrm{neutrons} = 20 + 27 = 47\) Step 3: \(X = \textrm{Calcium (Ca)}\) (Element with 20 protons) The atomic symbol for this isotope is \(\left(_{20}^{47}\textrm{Ca}\right)\).

Step 6: f. Isotope with 29 protons and mass number 65

Step 1: \(Z = 29\) Step 2: \(A = 65\) Step 3: \(X = \textrm{Copper (Cu)}\) (Element with 29 protons) The atomic symbol for this isotope is \(\left(_{29}^{65}\textrm{Cu}\right)\).

Key Concepts

Isotopes

Isotopes are fascinating variations of elements that share the same number of protons but differ in the number of neutrons. They are like members of the same family, all carrying the same genetic material (protons) but having different characteristics (neutrons). This difference results in isotopes of the same element having different atomic masses, while their chemical properties remain largely the same.

• Example: Carbon has isotopes like Carbon-12 and Carbon-14, with 6 protons but different neutron counts: 6 and 8, respectively.
• Isotopes play a crucial role in fields such as archaeology, through radiocarbon dating, and in medicine, via radioactive isotopes used for diagnosis and treatment.

Understanding isotopes is key to learning how elements can exist in different forms and contribute uniquely to scientific advancements.

Mass Number

The mass number is a fundamental concept that represents the sum of protons and neutrons in an atomic nucleus. It essentially tells you how much an isotope "weighs," although the weight is more about the number of these heavy particles inside the nucleus.

• Mass number is symbolized by the letter \(A\).
• It differs from atomic weight, which is an average that includes all isotopes of an element found in nature.

By knowing the mass number, one can determine the number of neutrons in an isotope if the number of protons is known. This numerical sum is crucial in identifying isotopes and understanding their structure.

Protons and Neutrons

Protons and neutrons are the building blocks of an atomic nucleus. These subatomic particles are pivotal in determining the identity and stability of an element.

• Protons, indicated by \(Z\), dictate the element's identity. For instance, 27 protons mean the element is Cobalt.
• Neutrons contribute to the mass of an isotope but do not affect the chemical identity. Their presence can impact the stability and occasional radioactivity of isotopes.

Finding both protons and neutrons helps scientists calculate the mass number and identify specific isotopes of an element. This understanding is foundational in the study of atomic structure.

Element Identification

Identifying an element involves recognizing it by its atomic number, which is synonymous with the number of protons in its nucleus. This number defines the element and sets it apart from others in the periodic table.

• Atomic number \(Z\) is unique to each element, such as Hydrogen with \(Z = 1\) and Helium with \(Z = 2\).
• During element identification, the focus is on the number of protons, while isotopes are differentiated by the varying number of neutrons.

Correctly identifying elements is crucial for understanding the periodic table, chemical reactions, and the role each element plays in the universe. This knowledge forms the backbone of chemistry and many other scientific disciplines.