Question

For each of the questions, four choices have been provided. Select the correct alternative. An atom of an element has 9 electrons with \(1=0\) value, 18 electrons with \(\mathrm{l}=1\) value and 10 electrons with \(1=2\) value. Calculate the atomic number of the element. (a) 37 (b) 41 (c) 38 (d) 39

Short answer

Answer: The atomic number of the element is 37.

Step-by-step solution

Determine the number of electrons for each l value

We are given the following information: - 9 electrons with l=0 - 18 electrons with l=1 - 10 electrons with l=2

Calculate the total number of electrons

Now that we know how many electrons correspond to each l value, we can calculate the atomic number by summing up these electron counts: Total number of electrons = Electrons with l=0 + electrons with l=1 + electrons with l=2 Total number of electrons = 9 + 18 + 10 = 37

Select the correct alternative

As we have calculated the total number of electrons (atomic number) to be 37, the correct alternative is (a). Therefore, the atomic number of the element is 37.

Key concepts

Atomic Number

The atomic number of an element is a fundamental property that defines its identity. It is represented by the number of protons found in the nucleus of an atom of the element, and uniquely determines the chemical element. For a neutral atom, the atomic number is also equal to the number of electrons surrounding the nucleus. This crucial number helps us understand the position of the element in the periodic table and its chemical properties.
When you know the atomic number, you can easily determine which element you are dealing with using a periodic table. For instance, if an element has an atomic number of 37, it is Rubidium (Rb). The atomic number increases sequentially from the top left to the bottom right of the periodic table.
Understanding the atomic number is pivotal, as it relates directly to the electron configuration, which is key in predicting an element's chemical reactions and bonding.

Electron Configuration

Electron configuration describes the distribution of electrons in an atom's orbitals. It provides a method of indicating how electrons are configured within an atom, usually depicted using the electrons' principal energy levels and sublevels (s, p, d, f). This configuration provides insight into the chemical behavior of an atom.

• Each atom has a unique electron configuration that is determined by three rules: the Aufbau principle, the Pauli Exclusion Principle, and Hund's rule.
• The Aufbau principle states that electrons fill the lowest energy orbitals first before moving to higher ones.
• The Pauli Exclusion Principle indicates that each orbital can hold a maximum of two electrons with opposite spins.
• Hund's Rule states that electrons will fill an unoccupied orbital before they pair up in an occupied one.

For example, an element with 37 electrons will have an electron configuration of \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1\].
This configuration reflects the sequence in which electrons fill available energy levels, starting with the lowest.

Quantum Numbers

Quantum numbers are essential in understanding the arrangement of electrons in atoms. They describe unique properties of electrons and their orbitals:

• Principal Quantum Number (n): Indicates the main energy level occupied by the electron. It is a positive integer, and the higher the number, the further the electron is from the nucleus.
• Angular Momentum Quantum Number (l): Defines the shape of the orbital. It can range from 0 to (n-1). Different values correspond to different types of orbitals: s (l=0), p (l=1), d (l=2), and f (l=3).
• Magnetic Quantum Number (m_l): Specifies the orientation of the orbital in space. It ranges from -l to +l.
• Spin Quantum Number (m_s): Refers to the two spinning states of an electron: +1/2 or -1/2.

For the element with 37 electrons in the example, it notably includes orbitals with l-values 0, 1, and 2 with their respective electron counts. These quantum numbers collectively ensure each electron has a unique "address" within an atom, reinforcing the specific structure of electron clouds and how electrons are distributed.