List the sets of quantum numbers which describe all of the electrons possible in a 6p wave function (orbital):
I'm really having trouble figuring this out!
There isn't anything to understand. There are four (4) quantum numbers and they have rules to follow:
1. The value of n may be 1,2,3,4,5 or any whole number larger than 0 but may not be zero.
2. The value of l may be any whole number but may not be larger than n-1. Therefore, for n = 1, l may be zero. For n = 2, l may be 0 or 1. For n = 3, l may be 0, 1, or 2, etc. If l = 0 we call it an s electron. If l = 1 we call it a p electron. If l = 2 we call it a d electron and if l = 3 we call it an f electron.
3.The value of ml may have values from -l to +l, all in whole numbers, including zero.
4. The value of ms may be +/- 1/2.
Your question doesn't need all of this to answer it but I thought it might be useful to write ALL of the rules, then you apply these rules to the question.
6 is the n value.
p means l = 1
So we can have
n = 6
l = 1
ml = -1
Ms +1/2 and -1/2 (Two electrons here with values of n, l, m the same and the only difference is ms is +1/2 for 1 electron and -1/2 for the other.)
n = 6
l = 1
ml = 0
ms = +1/2 and -1/2 (Two more electrons here.)
n = 6
l = 1
ml = +1
ms = +1/2 and -1/2 (Two more electrons)
There are six electrons possible. That's all of the p electrons an atom can have for any given value of n
Remember these rules.
6p means n = 6 and p means l = 1.
ml = -l to +l in increments of 1 and that includes zero. In practice all that means is that ml can be -1, or 0, or +1.
Then remember that ms can be +/- 1/2 for each ml value.
I'm really bad at this, I still don't understand.
Yeah, I figured it out after I said I didn't understand. It's actually really easy. Thanks for all your help though!
To determine the sets of quantum numbers that describe all possible electrons in a 6p orbital, we need to consider the four quantum numbers: principle quantum number (n), azimuthal quantum number (l), magnetic quantum number (m_l), and spin quantum number (m_s).
1. Principle Quantum Number (n): The n quantum number represents the energy level or shell of an electron. For the 6p orbital, n = 6, as p orbitals belong to the 6th energy level.
2. Azimuthal Quantum Number (l): The l quantum number describes the shape or subshell of an orbital. For p orbitals, l = 1. Thus, in the 6p orbital, l = 1.
3. Magnetic Quantum Number (m_l): The m_l quantum number specifies the orientation of an orbital within its subshell. For p orbitals, m_l can have three possible values: -1, 0, and 1. This means that there are three distinct 6p orbitals, which can be represented as 6p_x, 6p_y, and 6p_z.
4. Spin Quantum Number (m_s): The m_s quantum number describes the spin state of an electron. It can have two possible values: +1/2 (spin-up) and -1/2 (spin-down).
Combining the values of these quantum numbers, we can determine the sets of quantum numbers for all possible electrons in a 6p orbital:
1st electron:
n = 6, l = 1, m_l = -1, m_s = +1/2
2nd electron:
n = 6, l = 1, m_l = -1, m_s = -1/2
3rd electron:
n = 6, l = 1, m_l = 0, m_s = +1/2
4th electron:
n = 6, l = 1, m_l = 0, m_s = -1/2
5th electron:
n = 6, l = 1, m_l = +1, m_s = +1/2
6th electron:
n = 6, l = 1, m_l = +1, m_s = -1/2
So, these six sets of quantum numbers represent all the possible electrons in a 6p orbital.