Respuesta :
Answer : There are three possible values of 'l' which are 2, 3 and 4.
Solution : Given,
n = 5
[tex]m_l=-2[/tex]
There are 4 quantum numbers :
- Principle quantum number = n
values are 1, 2, 3, 4, .........
- Azimuthal quantum number = l
values are 0 to (n-1)
- Magnetic quantum number = [tex]m_l[/tex]
values are +l to -l
- Spin quantum number = [tex]m_s[/tex]
values are [tex]+\frac{1}{2}[/tex] to [tex]-\frac{1}{2}[/tex]
when n = 5 then the value of l are,
l = 0, 1, 2, 3, 4
At l = 0, [tex]m_l=0[/tex]
At l = 1, [tex]m_l=+1,0,-1[/tex]
At l = 2, [tex]m_l=+2,+1,0,-1,-2[/tex]
At l = 3, [tex]m_l=+3,+2,+1,0,-1,-2,-3[/tex]
At l = 4, [tex]m_l=+4,+3,+2,+1,0,-1,-2,-3,-4[/tex]
So, when [tex]m_l=-2[/tex] then the possible values of l are,
l = 2, 3, 4
The possible values of l for the orbital having n = 5 and [tex]{m_l}=- 2[/tex] are [tex]\boxed{2,3\;{\text{and}}\;4}[/tex] .
Further explanation:
The size, energy, shape, and orientation of an orbital depend upon four quantum numbers. These 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 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]\left( {{m_5}}\right)[/tex]: It represents the direction of electron spin. Its value can be [tex]-\dfrac{1}{2}[/tex] or [tex]+\dfrac{1}{2}[/tex].
The value of principal quantum number (n) is 5. This indicates the value of angular momentum quantum number (l) ranges from 0 to 4 (5-1). The value of magnetic quantum number [tex]\left( {{m_l}}\right)[/tex] for different values of l are as follows:
When l = 0, [tex]{m_l}[/tex] = 0
When l = 1, [tex]{m_l}[/tex]= -1, 0, +1
When l = 2, [tex]{m_l}[/tex] = -2, -1, 0, +1, +2
When l = 3, [tex]{m_l}[/tex]= -3, -2, -1, 0, +1, +2, +3
When l = 4, [tex]{m_l}[/tex]= -4, -3, -2, -1, 0, +1, +2, +3, +4
But the given value of [tex]{m_l}[/tex] is -2. So the possible values of l for this orbital is 2, 3 and 4.
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, n, l, ml, ms, principal quantum number, angular momentum quantum number, electron spin quantum number, magnetic quantum number, n = 5, ml=-2, orbital, hydrogen atom, possible values.
