Respuesta :
Quantum numbers are a set of numbers used to describe the position and the motion of an electron within the atom.
Quantum numbers are as follows:
n-quantum number : represents the energy level
l-quantum number : represents the orbital (s,p,d,f,....)
ml-quantum number : represents the position of the electron within the orbital
ms-quantum number : represents the spin of the electron within the electron pair.
Bromine has an atomic number of 35.
So, the configuration of the Br is: [Ar] 3d10 4s2 4p5
Now, we will add one electron to the Br to be a negative ion (Br-).
This extra electron will be added to the 4th principle level in the p-orbital.
So, the quantum numbers that represent the extra electron added to the Br will be as follows:
n = 4 (it is added in the 4th principle level)
l = 1 (it is added in the p-orbital)
ml = 1
ms = -1/2
Quantum numbers are as follows:
n-quantum number : represents the energy level
l-quantum number : represents the orbital (s,p,d,f,....)
ml-quantum number : represents the position of the electron within the orbital
ms-quantum number : represents the spin of the electron within the electron pair.
Bromine has an atomic number of 35.
So, the configuration of the Br is: [Ar] 3d10 4s2 4p5
Now, we will add one electron to the Br to be a negative ion (Br-).
This extra electron will be added to the 4th principle level in the p-orbital.
So, the quantum numbers that represent the extra electron added to the Br will be as follows:
n = 4 (it is added in the 4th principle level)
l = 1 (it is added in the p-orbital)
ml = 1
ms = -1/2
The possible values of all quantum numbers for the electron gained by Br atom to form [tex]{\text{B}}{{\text{r}}^-}[/tex] is [tex]\boxed{n=4,\;l=1,\;{m_l}=1,\;{m_s}=-\frac{1}{2}}[/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 integer (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). (Refer to the table in the attached image)
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 atomic number of bromine (Br) is 35 and its electronic configuration is [tex]\left[ {{\text{Ar}}} \right]\;3{d^{10}}4{s^2}4{p^5}[/tex]. When it gains an electron, it forms [tex]{\text{B}}{{\text{r}}^ - }[/tex] whose electronic configuration becomes [tex]\left[ {{\text{Ar}}} \right]\;3{d^{10}}4{s^2}4{p^6}[/tex].
The principal electron shell in [tex]{\text{B}}{{\text{r}}^ - }[/tex] is 4p. So its principal quantum number for the added electron in [tex]{\text{B}}{{\text{r}}^ - }[/tex] is 4.
The angular momentum quantum number for p orbital is 1. So the value of l for the added electron in [tex]{\text{B}}{{\text{r}}^ - }[/tex] is 1.
The value of magnetic quantum number for the electron in [tex]{\text{B}}{{\text{r}}^ - }[/tex] ranges from -1 to 1, including 0. But by convention this electron is added to [tex]{p_z}[/tex] orbital so the value of [tex]{m_l}[/tex] for the added electron in [tex]{\text{B}}{{\text{r}}^ - }[/tex] is 1.
The spin quantum number has two values, either [tex]+ \frac{1}{2}[/tex] or [tex]- \frac{1}{2}[/tex]. But the electron added in Br is the second electron being added to [tex]{p_z}[/tex] orbital so by convention, the value of [tex]{m_s}[/tex] for the added electron in [tex]{\text{B}}{{\text{r}}^-}[/tex] is [tex]{\mathbf{ - }}\frac{{\mathbf{1}}}{{\mathbf{2}}}[/tex].
The possible set of four quantum numbers for the electron gained by Br atom to form [tex]{\text{B}}{{\text{r}}^ - }[/tex] is n = 4, l = 1, [tex]{m_l} = 1[/tex] and [tex]{m_s} = - \frac{1}{2}[/tex].
Learn more:
1. Allowed values of [tex]{m_l}[/tex]: https://brainly.com/question/2920448
2. Calculation of volume of gas: https://brainly.com/question/3636135
Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Structure of the atom
Keywords: quantum numbers, Br, Br-, electron, 35, electronic configuration, n, l, ml, ms, principal quantum number, angular momentum quantum number, electron spin quantum number, magnetic quantum number, n = 4, ml=1, ms=-1/2, l=1.
