Problem 6 - Chemistry and Chemical Reactivity

Question

Give the complete symbol \(\left(_{Z}^{A} X\right),\) including atomic number and mass number, of (a) a nickel atom with 31 neutrons, (b) a plutonium atom with 150 neutrons, and (c) a tungsten atom with 110 neutrons.

Step-by-Step Solution

Answer

(a) \(_{28}^{59} \text{Ni}\), (b) \(_{94}^{244} \text{Pu}\), (c) \(_{74}^{184} \text{W}\).

Step 1: Understanding the Problem

To find the complete symbol \(\left(_{Z}^{A} X\right)\), we need the atomic number \(Z\) (number of protons) and the mass number \(A\) (number of protons plus number of neutrons). Given are the neutron numbers for nickel, plutonium, and tungsten atoms.

Step 2: Finding Nickel's Atomic Information

1. Nickel (Ni) has an atomic number \(Z = 28\). 2. The neutron number is given as 31.3. Calculate the mass number \(A\): \[ A = Z + \text{Number of Neutrons} = 28 + 31 = 59 \]4. Therefore, the complete symbol for nickel is \(\left(_{28}^{59} \text{Ni}\right)\).

Step 3: Finding Plutonium's Atomic Information

1. Plutonium (Pu) has an atomic number \(Z = 94\).2. The neutron number is given as 150.3. Calculate the mass number \(A\): \[ A = Z + \text{Number of Neutrons} = 94 + 150 = 244 \]4. Therefore, the complete symbol for plutonium is \(\left(_{94}^{244} \text{Pu}\right)\).

Step 4: Finding Tungsten's Atomic Information

1. Tungsten (W) has an atomic number \(Z = 74\).2. The neutron number is given as 110.3. Calculate the mass number \(A\): \[ A = Z + \text{Number of Neutrons} = 74 + 110 = 184 \]4. Therefore, the complete symbol for tungsten is \(\left(_{74}^{184} \text{W}\right)\).

Key Concepts

Atomic Number

In chemistry and physics, the atomic number is one of the most fundamental properties of an element. It is often denoted by the letter \( Z \) and represents the number of protons in the nucleus of an atom. Since each element is defined by the number of protons, the atomic number is unique to each element.
For example, nickel has an atomic number of 28, which means every nickel atom contains 28 protons. Understanding the atomic number is crucial because:

• It determines the element's identity and position in the periodic table.
• It is equal to the number of electrons in a neutral atom, affecting chemical behavior.

Hence, when identifying elements in exercises like this, always look up the atomic number to confirm the element's identity.

Mass Number

The mass number, denoted as \( A \), is another vital concept in understanding isotopes and their notation. Unlike the atomic number, the mass number is not fixed for an element as it represents the total count of protons and neutrons in an atom's nucleus. Thus, the formula is:
\[ A = Z + ext{Number of Neutrons} \]
The mass number helps to distinguish between different isotopes of the same element. For instance:

• Nitrogen-14 and Nitrogen-15 are both isotopes of nitrogen, differentiated by their mass numbers.
• Mass number helps in isotope notation, which provides information about the specific isotopic form.

When solving problems, calculating the mass number will give you the complete isotopic symbol of an element, such as \( \left(_{28}^{59} \text{Ni}\right) \) for nickel with 31 neutrons.

Neutron Number

The neutron number is the difference between mass number and atomic number. Neutrons are neutral particles in the nucleus and play a key role in the stability of atoms. Their number in an atom does vary, resulting in different isotopes for the same element.
The neutron number is calculated as:
\[ ext{Number of Neutrons} = A - Z \]
The neutron number influences the atomic mass and the stability of the nucleus. Key points about neutron numbers include:

• Different neutron numbers lead to isotopic variations.
• Some isotopes are stable, while others are radioactive.

For example, plutonium with an atomic number of 94 and 150 neutrons has the mass number 244, leading to its complete symbol \( \left(_{94}^{244} \text{Pu}\right) \). Understanding neutron numbers is vital in calculating isotopes and analyzing nuclear reactions.