Problem 17 - Chemistry Matter and Change

Question

Challenge An atom has a mass number of 55. Its number of neutrons is the sum of its atomic number and five. How many protons, neutrons, and electrons does this atom have? What is the identity of this atom?

Step-by-Step Solution

Answer

The atom has 25 protons, 30 neutrons, and 25 electrons, making it an atom of manganese (Mn).

Step 1: Write down the formula for mass number

The mass number (A) is given by the sum of the number of protons (Z) and the number of neutrons (N). The formula is: A = Z + N.

Step 2: Write the equation for the number of neutrons

We are given that the number of neutrons (N) is equal to the sum of the atomic number (Z) and five, so we can write the equation: N = Z + 5.

Step 3: Substitute N in the mass number formula

Now that we have the equation for N, we can substitute it back into the mass number formula: A = Z + (Z + 5), which simplifies to A = 2Z + 5.

Step 4: Solve for Z (the atomic number)

We are given the mass number A = 55, so we can plug this value into the equation: 55 = 2Z + 5. Solving for Z, we get: 2Z = 55 - 5 2Z = 50 Z = 25

Step 5: Calculate N (the number of neutrons)

Substitute the value of Z (25) back into the equation N = Z + 5, we get: N = 25 + 5 N = 30

Step 6: Determine the number of electrons

In a neutral atom, the number of protons (Z) is equal to the number of electrons. So, this atom has 25 electrons.

Step 7: Identify the atom

Now that we have the atomic number (Z = 25), we can identify the element using the periodic table. The element with an atomic number of 25 is manganese (Mn). Finally, we've found that this atom has 25 protons, 30 neutrons, and 25 electrons, and it is an atom of manganese (Mn).

Key Concepts

Mass Number

The mass number is a key concept in understanding atomic structure. It is the total count of protons and neutrons within an atom's nucleus. Represented by the symbol \( A \), the mass number is expressed in the formula \( A = Z + N \), where \( Z \) is the number of protons, and \( N \) represents neutrons. This number helps distinguish between different isotopes of the same element since isotopes differ in neutron counts while having the same number of protons. If you know the mass number and the atomic number, you can easily determine the neutron count, which is crucial for identifying isotopes and understanding atomic identity.

Atomic Number

The atomic number is a fundamental characteristic of an element. It represents the number of protons in an atom's nucleus and is denoted by the symbol \( Z \). Each element on the periodic table has a unique atomic number. For instance, hydrogen has an atomic number of 1, which means it has 1 proton. In a neutral atom, the number of electrons is equal to the atomic number, balancing the positive charge of the protons. Determining the atomic number is essential, as it defines the element's position on the periodic table and its chemical properties. In our exercise, solving for \( Z \) allowed us to identify the element as manganese, which has an atomic number of 25.

Neutrons

Neutrons are uncharged particles found in the nucleus of an atom, alongside protons. They play a crucial role in the atom's stability and mass. The number of neutrons can be found using the formula \( N = A - Z \), where \( A \) is the mass number, and \( Z \) is the atomic number.In the given problem, the number of neutrons was a direct expression involving the atomic number: \( N = Z + 5 \). By first calculating \( Z \) and using this equation, the number of neutrons was determined to be 30. Neutrons are vital in determining atomic structure, impacting isotopes and nuclear reactions.

Protons

Protons are positively charged particles located in an atom's nucleus. They define the atomic number and thus the element itself. The number of protons is equal to the atomic number \( Z \), and in neutral atoms, it also matches the electron count.For example, the exercise establishes that the atom has 25 protons since \( Z = 25 \). These protons not only determine the identity of the element, but also substantially contribute to the atomic mass. Besides, protons, along with neutrons, define the structure of an atom and influence its chemical properties and bonding behavior.

Electrons

Electrons are negatively charged particles that orbit an atom's nucleus. In a neutral atom, their number equals the number of protons, helping to balance the atom's overall charge. Electrons play a crucial role in chemical reactions and bonding due to their ability to be shared or transferred between atoms. Regarding the problem, they confirm the atom's neutrality since the number of electrons matches the number of protons, 25 in this case, affirming that the atom is manganese. Understanding electron distribution is key to grasping an element's reactivity and its place in the electronegativity scale.