When compared with the energy of an electron in the first shell of a carbon atom, the energy of an electron in the second shell of a carbon atom is [tex]\boxed{\left( {\text{2}} \right){\text{ greater}}}[/tex].
Further explanation:
Quantum numbers:
Quantum numbers govern the size, energy, shape, and orientation of an orbital. The four quantum numbers are as follows:
1. Principal Quantum Number (n): It denotes the principle electron shell. The values of n are positive integers (1, 2, 3,…).
2. Angular Momentum Quantum Number (l): It represents the shape of an orbital. The value of l is an integer from 0 to (n-1).
3. Magnetic Quantum Number[tex]\left( {{m_l}} \right)[/tex]: This quantum number represents the orientation of the orbital in space. The value of [tex]{m_l}[/tex]lies between –l to +l. The formula to calculate the value of [tex]{m_l}[/tex] is as follows:
[tex]{m_l} = - l,( - l + 1),.....,0,1,2,.....,(l - 1),l[/tex]
Therefore, the total number of [tex]{m_l}[/tex] values for a given value of l is 2l+1.
4. Electron Spin Quantum Number[tex]({m_s})[/tex]: It represents the direction of the electron spin. Its value can be [tex]+ \frac{1}{2}[/tex]or[tex]- \frac{1}{2}[/tex].
The formula to calculate the energy of an electron in an atom is as follows:
[tex]{{\text{E}}_{\text{n}}} = \frac{{ - 13.6{{\text{Z}}^2}}}{{{{\text{n}}^{\text{2}}}}}{\text{eV}}[/tex] …… (1)
Here,
E is the energy of an electron.
Z is the atomic number of atom.
n is the principal quantum number.
Calculation of energy of an electron in the first shell of carbon atom.
The value of Z is 6.
The value of n is 1.
Substitute these values in equation (1) to calculate the energy of electron in the first shell.
[tex]\begin{aligned}{{\text{E}}_2}&=\frac{{ - 13.6{{\left( 6 \right)}^2}}}{{{{\left( 1 \right)}^{\text{2}}}}}{\text{eV}}\\&=\boxed{-489.6\;{\text{eV}}}\\\end{aligned}[/tex]
Calculation of energy of an electron in the second shell of carbon atom.
The value of Z is 6.
The value of n is 2.
Substitute these values in equation (1) to calculate the energy of an electron in the second shell.
[tex]\begin{aligned}{{\text{E}}_1}&=\frac{{-13.6{{\left( 6 \right)}^2}}}{{{{\left( 2 \right)}^{\text{2}}}}}{\text{eV}\\&=\boxed{-122.{\text{4 eV}}}\\\end{aligned}[/tex]
The negative sign in the energy of the electron in both the shells indicates that the electron is bound to the nucleus of an atom. So the energy of electron in the second shell of carbon atom is greater than its energy in the first shell of carbon atom and therefore option (2) is correct.
Learn more:
1. Which transition is associated with the greatest energy change? https://brainly.com/question/1594022
2. Describe the spectrum of elemental hydrogen gas: https://brainly.com/question/6255073
Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Atomic structure
Keywords: energy of electron, n^2, Z^2, -13.6, n, Z, -122.4 eV, -489.6 eV, 6, 1, 2, first shell, second shell.