Problem 11 - Chemistry and Chemical Reactivity

Question

Give the complete symbol \(\left(\frac{4}{z} \mathrm{X}\right)\) for each of the following atoms: (a) potassium with 20 neutrons, (b) krypton with 48 neutrons, and (c) cobalt with 33 neutrons.

Step-by-Step Solution

Answer

(a) \(\left(\frac{39}{19} \mathrm{K}\right)\), (b) \(\left(\frac{84}{36} \mathrm{Kr}\right)\), (c) \(\left(\frac{60}{27} \mathrm{Co}\right)\)."

Step 1: Understanding Atomic Symbols

The symbol \( \left(\frac{A}{Z} \mathrm{X}\right) \) represents an atomic symbol where \(A\) is the mass number (total number of protons and neutrons), \(Z\) is the atomic number (number of protons), and \(X\) is the element's symbol.

Step 2: Potassium with 20 Neutrons

Potassium (K) has an atomic number (\(Z\)) of 19, indicating it has 19 protons. The mass number (\(A\)) is the sum of protons and neutrons. With 20 neutrons, \(A = 19 + 20 = 39\). Thus, the symbol is \( \left(\frac{39}{19} \mathrm{K}\right) \).

Step 3: Krypton with 48 Neutrons

Krypton (Kr) has an atomic number (\(Z\)) of 36, indicating it has 36 protons. The mass number (\(A\)) is the sum of protons and neutrons. With 48 neutrons, \(A = 36 + 48 = 84\). Thus, the symbol is \( \left(\frac{84}{36} \mathrm{Kr}\right) \).

Step 4: Cobalt with 33 Neutrons

Cobalt (Co) has an atomic number (\(Z\)) of 27, indicating it has 27 protons. The mass number (\(A\)) is the sum of protons and neutrons. With 33 neutrons, \(A = 27 + 33 = 60\). Thus, the symbol is \( \left(\frac{60}{27} \mathrm{Co}\right) \).

Key Concepts

Mass Number

The mass number is a fundamental concept crucial for understanding atomic symbols. It is denoted by the letter \( A \) in atomic notation and represents the total sum of protons and neutrons in an atom's nucleus. This value gives us the approximate mass of an atom since protons and neutrons each have a mass of about one atomic mass unit (amu). Every atom has a specific mass number, which can change depending on the number of neutrons it contains. For example, isotopes are variations of elements with the same number of protons but different numbers of neutrons, leading to different mass numbers.

• Mass number \( A = \text{number of protons} + \text{number of neutrons} \).
• Critical for identifying isotopes and characterizing atomic weight.
• Not to be confused with atomic weight, which is an average of all isotopic masses.

Atomic Number

The atomic number, represented by \( Z \), is the count of protons in the nucleus of an atom. This number is integral to an element's identity on the periodic table. Each element has a unique atomic number, which determines its position on the periodic table and its chemical properties. The atomic number serves as a fingerprint for the element - no two elements share the same atomic number.

• Atomic number \( Z \) equals the number of protons in an atom.
• Defines the element and its chemical behavior in reactions.
• Found at the bottom of the atomic symbol in standard notation \( \left( \frac{A}{Z} \right) \).

Knowing the atomic number helps students quickly determine the element involved in nuclear reactions or when analyzing chemical compounds. It is also the same as the number of electrons in a neutrally charged atom, which is crucial for understanding electronic configurations and bonding.

Neutrons

Neutrons are neutrally charged particles found in the nucleus of an atom. They play a significant role in the stability and overall mass of the atom. While not influencing the electrical charge, neutrons contribute to the mass number and help differentiate isotopes. The number of neutrons in an atom can vary even within the same element, leading to the formation of different isotopes, such as Carbon-12 and Carbon-14. This variance affects the atomic mass and can alter the nucleus's stability.

• Neutrons add mass to the atom but do not affect the charge.
• Crucial for forming isotopes, which are variants of elements with the same atomic number but different mass numbers.
• The neutron's presence impacts nuclear reactions and radioactive decay.

Understanding neutrons is essential for comprehending how atoms of the same element can differ in mass and behavior, especially in nuclear chemistry and physics. The discovery of neutrons has immensely expanded our ability to understand and manipulate atomic structures effectively.