How to Find Valence Energy Level: A Comprehensive Guide

Understanding the valence energy level is crucial when studying the properties and behavior of atoms and molecules. The valence energy level refers to the outermost energy level or shell of an atom, which contains the valence electrons. Valence electrons are the electrons involved in chemical bonding and determining the reactivity of an atom. In this blog post, we will explore how to find the valence energy level, step by step, using examples, formulas, and mathematical expressions.

How to Determine the Valence Energy Level

Identifying the Energy Level of Valence Electrons

To determine the valence energy level, we first need to identify the energy level or shell in which the valence electrons reside. In an atom, the energy levels are represented by numbers, with the first energy level being closest to the nucleus. The energy levels are often denoted by the letters K, L, M, N, and so on.

The valence energy level is the highest energy level occupied by electrons in an atom. This means that the valence energy level will be the highest numbered energy level with electrons. For example, if an atom has electrons in the 2nd and 3rd energy levels, the valence energy level will be the 3rd energy level (N).

Determining the Number of Valence Electrons

Once we have identified the valence energy level, we need to determine the number of valence electrons. Valence electrons are the electrons present in the valence energy level. The number of valence electrons can be determined by looking at the group number of the element in the periodic table.

For elements in groups 1 and 2, the number of valence electrons is equal to the group number. For example, sodium (Na) is in group 1, so it has 1 valence electron. Calcium (Ca) is in group 2, so it has 2 valence electrons.

For elements in groups 13 to 18, the number of valence electrons can be determined by subtracting the group number from 18. For example, oxygen (O) is in group 16, so it has 18 – 16 = 2 valence electrons. Chlorine (Cl) is in group 17, so it has 18 – 17 = 1 valence electron.

Locating the Valence Electrons on the Energy Level

To locate the valence electrons on the energy level, we need to distribute the valence electrons in the electron configuration. The electron configuration represents the arrangement of electrons in an atom’s energy levels and orbitals.

For example, let’s consider the element carbon (C). Carbon is in group 14, so it has 4 valence electrons. The electron configuration of carbon is 1s2 2s2 2p2. This means that there are 2 electrons in the 1st energy level (1s), 2 electrons in the 2nd energy level (2s), and 2 electrons in the 2nd energy level’s p orbital (2p).

The valence electrons in carbon are located in the 2nd energy level (2s and 2p orbitals). In this case, the valence energy level is the 2nd energy level (L).

Practical Examples of Finding Valence Energy Level

How to Find the Valence Energy Level of Iron (Fe)

Let’s take another example to solidify our understanding. Iron (Fe) is in group 8 of the periodic table. To find the valence energy level of iron, we need to determine its electron configuration. The electron configuration of iron is $Ar$ 3d6 4s2.

From the electron configuration, we can see that iron has 2 valence electrons in the 4th energy level (4s orbital). Therefore, the valence energy level of iron is the 4th energy level (N).

Identifying the Group with a Full Energy Level where the Valence Electrons are Located

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Sometimes, the valence energy level can be a full energy level. This happens when the atom has achieved a stable electron configuration by filling up the previous energy levels.

For example, let’s consider the noble gas neon (Ne). Neon is in group 18 of the periodic table and has the electron configuration 1s2 2s2 2p6. In this case, the valence energy level is the 2nd energy level (L), which is completely filled with 8 electrons.

Common Misconceptions and Challenges in Finding Valence Energy Level

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Misunderstanding the Valence Charge

One common misconception is to confuse the valence charge with the valence energy level. The valence charge refers to the electrical charge carried by an atom or ion, which is determined by the number of valence electrons gained or lost during chemical reactions. On the other hand, the valence energy level refers to the outermost energy level of an atom that contains the valence electrons.

Confusion between Energy Levels and Valence Electrons

Another challenge is the confusion between energy levels and valence electrons. It is important to understand that the energy levels represent the different shells or orbitals in an atom, while valence electrons are the electrons present in the outermost energy level. The valence energy level is the highest numbered energy level with electrons, and the valence electrons determine the chemical properties of an atom.

Finding the valence energy level is essential for understanding the behavior of atoms and molecules. By identifying the energy level of valence electrons, determining the number of valence electrons, and locating them on the energy level, we can gain insights into the chemical properties and reactivity of different elements. Remember to consider the group number and electron configuration when finding the valence energy level.

Numerical Problems on how to find valence energy level

Problem 1:

A particle in a one-dimensional box has a potential energy of 50 eV. Determine the valence energy level for this particle.

Solution:

Given:
Potential energy, $V = 50$ eV

The energy levels for a particle in a one-dimensional box are given by the equation:

$E_n = \frac{n^2h^2}{8mL^2}$

Where:
– $E_n$ is the energy level for the particle
– $n$ is the quantum number (1, 2, 3, …)
– $h$ is the Planck’s constant
– $m$ is the mass of the particle
– $L$ is the length of the box

To find the valence energy level, we need to determine the value of $n$ for which $E_n$ is closest to the potential energy $V$ .

Let’s calculate the valence energy level:

$E_n = \frac{n^2h^2}{8mL^2}$

Since the energy levels are discrete, we can start by assuming $n = 1$ and calculate $E_1$ :

$E_1 = \frac{1^2h^2}{8mL^2}$

Next, we can increase $n$ by 1 and calculate $E_2$ :

$E_2 = \frac{2^2h^2}{8mL^2}$

We continue this process until we find the energy level that is closest to the given potential energy $V$ .

Problem 2:

A hydrogen atom in its ground state has an energy of -13.6 eV. Determine the valence energy level for the hydrogen atom.

Solution:

Given:
Energy of the hydrogen atom in ground state, $E = -13.6$ eV

The energy levels for a hydrogen atom are given by the equation:

$E_n = -\frac{13.6}{n^2}$

Where:
– $E_n$ is the energy level for the hydrogen atom
– $n$ is the principal quantum number (1, 2, 3, …)
– -13.6 eV is the energy of the hydrogen atom in ground state

To find the valence energy level, we need to determine the value of $n$ for which $E_n$ is closest to the given energy $E$ .

Let’s calculate the valence energy level:

$E_n = -\frac{13.6}{n^2}$

Since the energy levels are discrete, we can start by assuming $n = 1$ and calculate $E_1$ :

$E_1 = -\frac{13.6}{1^2}$

Next, we increase $n$ by 1 and calculate $E_2$ :

$E_2 = -\frac{13.6}{2^2}$

We continue this process until we find the energy level that is closest to the given energy $E$ .

Problem 3:

An electron in a harmonic oscillator has an energy of 4.5 eV. Determine the valence energy level for this electron.

Solution:

Given:
Energy of the electron in a harmonic oscillator, $E = 4.5$ eV

The energy levels for a harmonic oscillator are given by the equation:

$E_n = \left(n + \frac{1}{2}\right)h\nu$

Where:
– $E_n$ is the energy level for the electron
– $n$ is the quantum number (0, 1, 2, …)
– $h$ is the Planck’s constant
– $\nu$ is the frequency of the harmonic oscillator

To find the valence energy level, we need to determine the value of $n$ for which $E_n$ is closest to the given energy $E$ .

Let’s calculate the valence energy level:

$E_n = \left(n + \frac{1}{2}\right)h\nu$

Since the energy levels are discrete, we can start by assuming $n = 0$ and calculate $E_0$ :

$E_0 = \left(0 + \frac{1}{2}\right)h\nu$

Next, we increase $n$ by 1 and calculate $E_1$ :

$E_1 = \left(1 + \frac{1}{2}\right)h\nu$

We continue this process until we find the energy level that is closest to the given energy $E$ .

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