The electron excitation in physics is the amount of energy required to eliminate an electron (or an atom in the outermost energy level) from a lower energy level to higher energy or excited energy level. Excitation is the addition of a discrete amount of energy generally known as the excitation energy, to a system such as an atomic nucleus, an atom, or a molecule which will further result in its alteration, ordinarily from the condition of lowest energy i.e., ground state to one of higher energy i.e., excited state. In this article, we will learn about the excitation, meaning of excitation and what is excitation energy in detail.
Excitation Meaning:
Now, let us have a look at what is excitation and what is the excited state of an atom in detail. Excitation is a process during which an electron transit from a lower level to a higher level. In general, excitation is often referred to as the jumping of an electron from the ground state to an immediate higher energy level is known as excitation. Thus, excitation meaning just elaborates on the transition of an electron from one level to another.
In atomic physics, the excitation meaning or the excitation energy is defined as it is the required maximum energy to make an atom in the outermost orbit transit or jump from one level to another (lower energy level to higher energy level). The molecules in the excited state of an atom are always unstable and will be having a very short lifetime such that they lose their gained energy and get de-excited.
Excitation Energy:
We know that an atm consists of n number of energy levels. Every orbit of an atom will be having different energy levels. Consider an atom with the nucleus at its centre, and the electrons are revolving around the nucleus in discrete orbits assigned with principal quantum number n=1, n=2, n=3, and so on and the respective orbits are named as K, L, M, and so on. The same orbits can be expressed in the energy levels such that the lowest orbit is known as the ground state (here we assumed hydrogen atom and hence n=1 state as the ground state) and the highest possible orbit around the nucleus will our excited state or higher energy level, usually an atom will be having n number of energy levels.
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So, the amount of energy required to excite an electron in the ground state to the immediate higher state is known as the excitation energy of that electron. The amount of excitation energy depends on the spacing between the two levels, wider energy levels will require more energy and if the spacing between two energy levels is small or short then it will not require much energy to excite an electron from a lower state to a higher state.
Excitation Energy Formula:
Therefore, the excitation formula can be calculated using the below formula. We know that the excitation energy is the amount of energy required for an electron to transit from a lower energy state to a higher energy state, then the excitation energy formula can be formulated as the difference between the energy of lower level (ground state) to higher energy level. Mathematically, we write:
\[\Rightarrow E_{excited} = \Delta E = E_{higher} - E_{lower}\]…….(1)
Since we are assuming a hydrogen atom, thus the energy of any level is given by:
\[\Rightarrow E_{n} = 13.6 z^2 (\frac {1}{n_{1}^2 - \frac {1}{n_{2}^2}})\]…….(2)
Or
\[\Rightarrow E_{n} = \frac {13.6}{n^2} \]……(3)
Where,
Z - The atomic number and since here it’s hydrogen atom we say Z = 1.
n1 and n2 - The principal quantum numbers of considered energy levels
Therefore, equation (1) is known as the Excitation energy formula and equation (2) and (3) are the formula required to calculate the energies of the exciting individual level.
Examples:
Calculate the first excitation energy of an electron in the hydrogen atom.
Sol:
Given, that a hydrogen atom is considered and we are asked to determine its first excited state energy. First excitation energy is the amount of energy required for an electron to excite from n=1 i.e., ground state to n=2 i.e., first excited state.
Given,
The atomic number of hydrogen atom = Z = 1
We know that the excitation energy is given by,
\[\Delta E = E_2-E_1\]……(1)
Now, the energy of the hydrogen atom is calculated by using the formula:
\[\Rightarrow E_{n} = \frac {-13.6}{n^2} \times eV \]…….. (2)
Where,
n - The principal quantum numbers of considered energy levels
Thus,
\[\Rightarrow E_{1} = \frac {-13.6}{1^2} eV = -13.6 eV\]
\[\Rightarrow E_{2} = -\frac {13.6}{2^2} eV = -3.4 eV\]
Substituting values E1 and E2 in equation and simplify:
\[\Rightarrow \Delta E = -3.4 - (-13.6)= 10.2 eV\]
Therefore, the first excitation energy of an electron is given by 10.2 eV.
The excitation energy of a hydrogen-like ion in its first excited state is 40.8 eV. Then, estimate the required amount of energy to eliminate the electron from the ion in its ground state.
Sol:
Given, that we have a hydrogen-like ion such that its first excitation energy is 40.8 eV. We are asked to determine the amount of energy required to eliminate an electron from the ion in its ground state.
Given that,
The first excited energy = \[\Delta\] E = 40.8 eV
We know that the excitation energy of an atom is calculated using the formula,
\[\Rightarrow \Delta E = 13.6 z^2 (\frac {1}{n_{1}^2 - \frac {1}{n_{2}^2}})\]…..(1)
Where,
Z - The atomic number and since here it’s a hydrogen-like atom we have to determine its value
n1 and n2 - The principal quantum numbers of considered energy levels and here n1 = 1 and n2 = 2
Therefore from equation (1), we have,
\[\Rightarrow 40.8 = 13.6Z^{2}[\frac{1}{1}-\frac{1}{2^{2}}]\]
\[\Rightarrow 40.8 = 10.2 Z^2\]
\[\Rightarrow 4 = Z^2\]
\[\Rightarrow Z = 2\]
Therefore, the atomic number of a hydrogen-like atom is Z = 2 and now to calculate the energy required to eliminate an electron from the ion is calculated by using the formula:
\[\Rightarrow E_n=\frac{-13.6}{n^{2}}Z^{2}eV\]…….. (1)
Where,
Z - The atomic number of atom
n-The principal quantum numbers of considered energy levels
Substituting, required values in equation (1), we get:
\[\Rightarrow E_1 = \frac{-13.6}{1^{2}}2^{2}eV\]
\[\Rightarrow E_1 = -13.6 \times 4 = -54.4eV \]
Therefore, the amount of energy required to eliminate an electron from a hydrogen-like ion is 54.4eV.
Calculate the first excited energy of a hydrogen-like atom whose atomic number is Z = 2.
Sol:
Given, a hydrogen-like atom is considered and we are asked to determine its first excited state energy. First excitation energy is the amount of energy required for an electron to excite from n=1 i.e., ground state to n=2 i.e., first excited state.
Given,
The atomic number of hydrogen atom = Z = 2
We know that the excitation energy is given by,
\[\Rightarrow \Delta E = E_2 - E_1 \]……(1)
Now, the energy of the hydrogen atom is calculated by using the formula:
\[\Rightarrow E_n = \frac{-13.6}{n^{2}}Z^{2}eV\]…….. (2)
Where,
Z - The atomic number of atom
n - The principal quantum numbers of considered energy levels
Thus,
\[\Rightarrow E_1 = \frac{-13.6}{1^{2}}2^{2}eV = -54.4 eV\]
\[\Rightarrow E_2 = \frac{-13.6}{2^{2}}2^{2}eV = -13.6 eV\]
Substituting values E1 and E2 in equation and simplify:
\[\Rightarrow \Delta E = -13.6 - (-54.4) = 40.8eV\]
Therefore, the first excitation energy of a hydrogen atom electron is given by 40.8 eV.
FAQs on Excitation
1. What is excited energy? How do we calculate the excited energy?
The excitation energy is the amount of energy required for an electron or an atom to jump from a lower energy level to a higher energy level. The excitation energy can be calculated as the difference between the energy of the lower level (ground state) to the higher energy level. Mathematically, we write:
\[\Rightarrow E_{excited} = \Delta E = E_{higher} - E_{lower}\]
2. What is excited potential?
The excitation potential is defined as it is the required maximum potential to make an atom in the outermost orbit transit or jump from one level to another (lower energy level to higher energy level).
