Problem 53 - Chemistry

Question

Write the atomic symbol \(\left({ }_{Z}^{A} X\right)\) for each of the following isotopes. a. \(Z=8\), number of neutrons \(=9\) b. the isotope of chlorine in which \(A=37\) c. \(Z=27, A=60\) d. number of protons \(=26\), number of neutrons \(=31\) e. the isotope of \(I\) with a mass number of 131 f. \(Z=3\), number of neutrons \(=4\)

Step-by-Step Solution

Answer

a. \(\left({ }_{8}^{17} \mathrm{O}\right)\) b. \(\left({ }_{17}^{37} \mathrm{Cl}\right)\) c. \(\left({ }_{27}^{60} \mathrm{Co}\right)\) d. \(\left({ }_{26}^{57} \mathrm{Fe}\right)\) e. \(\left({ }_{53}^{131} \mathrm{I}\right)\) f. \(\left({ }_{3}^{7} \mathrm{Li}\right)\)

Step 1: Determine Element and Mass Number

The atomic number Z is 8, which corresponds to Oxygen (O), and the number of neutrons is 9. To find the mass number A, we add the number of protons and neutrons: A = 8 + 9 = 17.

Step 2: Write Atomic Symbol for Oxygen Isotope

Using the determined element and mass number, we can write the atomic symbol as: \(\left({ }_{8}^{17} \mathrm{O}\right)\). #b. the isotope of chlorine in which A = 37#

Step 3: Determine Element and Atomic Number

The element is Chlorine (Cl) with a mass number A = 37. The atomic number Z for Chlorine is 17.

Step 4: Write Atomic Symbol for Chlorine Isotope

Using the given element and mass number, we can write the atomic symbol as: \(\left({ }_{17}^{37} \mathrm{Cl}\right)\). #c. Z = 27, A = 60#

Step 5: Determine Element

The atomic number Z is 27, which corresponds to Cobalt (Co).

Step 6: Write Atomic Symbol for Cobalt Isotope

Using the given element, atomic number, and mass number, we can write the atomic symbol as: \(\left({ }_{27}^{60} \mathrm{Co}\right)\). #d. number of protons = 26, number of neutrons = 31#

Step 7: Determine Element, Atomic Number, and Mass Number

The number of protons is 26, which corresponds to the element Iron (Fe) with the atomic number Z = 26. The number of neutrons is 31. To find the mass number A, add the number of protons and neutrons: A = 26 + 31 = 57.

Step 8: Write Atomic Symbol for Iron Isotope

Using the determined element and mass number, we can write the atomic symbol as: \(\left({ }_{26}^{57} \mathrm{Fe}\right)\). #e. the isotope of I with a mass number of 131#

Step 9: Determine Element and Atomic Number

The element is Iodine (I) with a mass number A = 131. The atomic number Z for Iodine is 53.

Step 10: Write Atomic Symbol for Iodine Isotope

Using the given element and mass number, we can write the atomic symbol as: \(\left({ }_{53}^{131} \mathrm{I}\right)\). #f. Z = 3, number of neutrons = 4#

Step 11: Determine Element and Mass Number

The atomic number Z is 3, which corresponds to Lithium (Li), and the number of neutrons is 4. To find the mass number A, we add the number of protons and neutrons: A = 3 + 4 = 7.

Step 12: Write Atomic Symbol for Lithium Isotope

Using the determined element and mass number, we can write the atomic symbol as: \(\left({ }_{3}^{7} \mathrm{Li}\right)\).

Key Concepts

Atomic Symbol

The atomic symbol is a compact way to represent an isotope of an element. This symbol encapsulates several pieces of crucial information in the format \( _{Z}^{A} X \). Here, \( Z \) represents the atomic number, \( A \) is the mass number, and \( X \) is the chemical symbol of the element. This notation is invaluable for quickly conveying the identity and atomic characteristics of an isotope.

• For example, the symbol \( _{8}^{17} \, O \) indicates the isotope of oxygen with an atomic number of 8 and a mass number of 17.
• This format allows chemists and physicists to succinctly communicate details about the atomic structure.

In essence, the atomic symbol acts as an atomic shorthand that embeds the identity, mass, and number of protons of an isotope, assisting in straightforward academic and laboratory discussions.

Mass Number

The mass number, denoted by \( A \), is the sum of protons and neutrons in an atom's nucleus. It provides insight into the total mass of the atom since both protons and neutrons have significant mass compared to electrons, which are almost negligible in this context.

• The mass number is crucial for isotope identification as isotopes of an element have the same number of protons but different numbers of neutrons, thus different mass numbers.
• Understanding mass numbers is essential for calculating the relative atomic mass of an element when multiple isotopes are involved.

For instance, when given the number of protons and neutrons, always remember that their sum equals the mass number: \( A = ext{protons} + ext{neutrons} \).

Atomic Number

The atomic number, denoted by \( Z \), is fundamental in defining the identity of an element. It tells us the number of protons in the nucleus of an atom, which determines the element itself.

• Each element on the periodic table has a unique atomic number.
• For example, Oxygen is always \( Z = 8 \), and Iron is \( Z = 26 \).

This number remains constant across all isotopes of an element, as isotopes only vary in the number of neutrons. Consequently, recognizing the atomic number is vital for identifying the element and understanding its chemical behavior and properties.

Neutrons

Neutrons are neutral particles within an atom's nucleus that contribute to the mass but not the charge. The number of neutrons can vary among isotopes of the same element, affecting the mass number but not the chemical properties.

• For example, Oxygen-17 has 9 neutrons, whereas the more common Oxygen-16 has only 8 neutrons.
• This variance leads to different isotopes having different mass numbers, thus affecting atomic mass calculations.

Neutrons play a crucial role in the stability of the nucleus, helping to offset the repulsive forces between protons that are due to their positive charge. Understanding neutrons is key to isotope differentiation and nuclear physics studies.

Protons

Protons are positively charged particles found in the nucleus of an atom, and they determine an element's identity due to their atomic number association. Each element has a distinct number of protons identifying it on the periodic table.

• Protons have a charge of \(+1\) and a mass slightly less than that of a neutron, though considerably greater than an electron.
• These particles play a critical role in the overall charge of the nucleus and the elemental identity.

In any atom, the number of protons equals the number of electrons in a neutral state, ensuring electrical neutrality. Protons are the backbone of an element, crucial for defining not only atomic structure but also chemical properties and periodic table placement.