Problem 17 - Chemistry and Chemical Reactivity

Question

Cobalt has three radioactive isotopes used in medical studies. Atoms of these isotopes have \(30,31,\) and 33 neutrons, respectively. Give the symbol for each of these isotopes.

Step-by-Step Solution

Answer

The isotopes are \( ^{57}_{27}\text{Co} \), \( ^{58}_{27}\text{Co} \), and \( ^{60}_{27}\text{Co} \).

Step 1: Understand the structure of Cobalt

Cobalt is a chemical element with the atomic number 27, which means it has 27 protons in its nucleus. The chemical symbol for Cobalt is 'Co'.

Step 2: Calculate the mass number for each isotope

The mass number (A) of an isotope is the sum of its protons and neutrons. For Cobalt, the mass number will be calculated using 27 protons and the given number of neutrons for each isotope.

Step 3: Calculate the mass number for the first isotope

For the first isotope with 30 neutrons, the mass number is calculated as: \[ A = 27 + 30 = 57 \]

Step 4: Calculate the mass number for the second isotope

For the second isotope with 31 neutrons, the mass number is: \[ A = 27 + 31 = 58 \]

Step 5: Calculate the mass number for the third isotope

For the third isotope with 33 neutrons, the mass number is: \[ A = 27 + 33 = 60 \]

Step 6: Write the symbols for each isotope

The symbol for an isotope is written as \(^{A}_{Z}\text{Element Symbol}\). For the isotopes of Cobalt:- The first isotope is \( ^{57}_{27}\text{Co} \)- The second isotope is \( ^{58}_{27}\text{Co} \)- The third isotope is \( ^{60}_{27}\text{Co} \)

Key Concepts

Cobalt

Cobalt is an essential chemical element that finds its place on the periodic table with the atomic number 27. This number is significant because it tells us that every cobalt atom has exactly 27 protons in its nucleus. Such atomic elements are defined by these protons as these particles determine the element's type and its position on the periodic table. The elemental symbol for Cobalt is 'Co', derived from its English name. Cobalt gets attention not only for its regular applications but also for its isotopes' roles in different scientific fields, especially in medicine. It is known for its ferromagnetic properties, meaning it can be magnetized and attracts iron, a trait useful in various industrial applications.
This element's magnetic quality, combined with the ability to form durable alloys, makes cobalt indispensable in creating cutting-edge technologies and materials.

Chemical Symbols

Chemical symbols are a shorthand way to represent elements. Each element is assigned a one or two-letter symbol, which is internationally recognized. These symbols are derived mainly from the English or Latin names of the elements. For instance, the chemical symbol for Cobalt is 'Co', reflecting its name directly.

• The capital letter always comes first, followed by a lowercase letter if needed.
• The symbol 'Co' indicates cobalt, while things like Medichlorians utilize completely different letters.
• No two elements share the same symbol, ensuring clarity.

Understanding chemical symbols is fundamental because they provide a universal language for scientists worldwide to communicate complex chemical concepts efficiently and without confusion.

Mass Number

The mass number of an atom is a significant concept in chemistry. It gives us the total count of both protons and neutrons in the nucleus of an atom. This value is critical because it helps differentiate isotopes of an element. Since protons determine the element, differences in neutron numbers result in isotopes.
For instance, cobalt isotopes discussed have 57, 58, and 60 as their mass numbers. This was calculated by adding the proton number (27 for cobalt) to each isotope’s specific neutron number (30, 31, and 33 respectively). This mass number is key because it affects the atomic mass and therefore the properties of the isotope.

• The mass number is denoted typically with the symbol 'A'.
• Mass number = Number of Protons + Number of Neutrons.
• Different isotopes have different mass numbers but the same atomic number.

Understanding the mass number aids in recognizing isotopes and their reactions in various chemical contexts.

Radioactive Isotopes

Radioactive isotopes, or radioisotopes, are atoms that have an unstable nucleus. This instability arises because their mass number due to extra neutrons makes the nucleus prone to decay, emitting radiation. This intrinsic property makes them invaluable in various scientific, medical, and industrial applications.
The isotopes of cobalt in particular have widespread uses in medicine, such as in imaging and cancer treatment. Radioactive isotopes can be very beneficial, but they also require careful handling to manage their energy emissions safely.

• Radioisotopes decay over time, releasing particles and energy.
• In medicine, they serve in diagnostic tools or treatment methods by targeting specific cells.
• They help in dating archaeological finds through radiometric dating techniques.

Recognizing the role and significance of radioactive isotopes like those of cobalt is essential for understanding their diverse applications and safety measures necessary in employing them.