For each electron in a ground-state Be atom, select the set of quantum numbers that represents it. Check all that apply.
n=1 l=0 ml=-1 ms= +1/2
n=1 l=0 ml=0 ms=-1/2
n=2 l=1 ml=0 ms= -1/2
n=1 l=0 ml=0 ms=+1/2
n=2 l=1 ml=1 ms=+1/2
n=2 1=0 ml=0 ms=+1/2
n=2 l=0 ml=0 ms=-1/2
n=2 l=0 ml=0 ms=-1
I know the top one and the last one aren't correct but I don't know about the others. The hint said,"Make sure you have chosen exactly four answers" why will it have 4?
Well, it's because we're dealing with a ground-state Be atom, which has 4 electrons. Each electron will have its own set of quantum numbers. So, when choosing the set of quantum numbers for each electron, we need to select exactly four answers to represent the four electrons in the ground-state Be atom. Hope that clears things up!
To determine which set(s) of quantum numbers represent the electrons in a ground-state Be atom, we need to understand the meaning of each quantum number.
1. Principal quantum number (n): This represents the energy level or shell in which the electron is located.
2. Azimuthal quantum number (l): This represents the shape of the electron's orbital within the energy level.
3. Magnetic quantum number (ml): This represents the orientation of the orbital within a particular energy level and shape.
4. Spin quantum number (ms): This represents the spin state of the electron.
For each electron in a ground-state Be atom, the maximum number of electrons that can be accommodated in each energy level, according to the formula 2n^2, is as follows:
- For n=1, maximum electrons = 2(1)^2 = 2
- For n=2, maximum electrons = 2(2)^2 = 8
When filling the electron orbitals, we follow the Aufbau principle, which states that electrons fill the lowest energy orbitals first. The order of filling is: 1s, 2s, 2p, 3s, 3p, 4s, etc.
Now let's analyze the provided sets of quantum numbers:
1. n=1, l=0, ml=-1, ms=+1/2: This set represents an electron in the 1s orbital. (Correct)
2. n=1, l=0, ml=0, ms=-1/2: This set represents an electron in the 1s orbital. (Correct)
3. n=2, l=1, ml=0, ms=-1/2: This set represents an electron in the 2p orbital. (Correct)
4. n=1, l=0, ml=0, ms=+1/2: This set represents an electron in the 1s orbital. (Correct)
5. n=2, l=1, ml=1, ms=+1/2: This set represents an electron in the 2p orbital. (Correct)
6. n=2, l=0, ml=0, ms=+1/2: This set represents an electron in the 2s orbital. (Incorrect)
7. n=2, l=0, ml=0, ms=-1/2: This set represents an electron in the 2s orbital. (Correct)
8. n=2, l=0, ml=0, ms=-1: This set represents an electron in the 2s orbital. (Incorrect)
From the analysis, options 1, 2, 3, and 7 are the correct sets of quantum numbers representing the electrons in a ground-state Be atom. Thus, the number of correct answers is 4, as hinted.
The electron configuration for a ground-state Be atom is 1s^2 2s^2. Each electron in an atom is described by a set of four quantum numbers: n (principal quantum number), l (azimuthal quantum number), ml (magnetic quantum number), and ms (spin quantum number).
Let's go through each option and determine if it represents a valid set of quantum numbers for an electron in a ground-state Be atom:
n=1 l=0 ml=-1 ms= +1/2: This set of quantum numbers represents an electron in the 1s orbital. (Valid)
n=1 l=0 ml=0 ms=-1/2: This set of quantum numbers also represents an electron in the 1s orbital. (Valid)
n=2 l=1 ml=0 ms= -1/2: This set of quantum numbers represents an electron in the 2p orbital. (Valid)
n=1 l=0 ml=0 ms=+1/2: This set of quantum numbers also represents an electron in the 1s orbital. (Valid)
n=2 l=1 ml=1 ms=+1/2: This set of quantum numbers represents an electron in the 2p orbital. (Valid)
n=2 1=0 ml=0 ms=+1/2: There seems to be a typographical error in the second term. Assuming it was supposed to be l=0, this set of quantum numbers represents an electron in the 2s orbital. (Valid)
n=2 l=0 ml=0 ms=-1/2: This set of quantum numbers represents an electron in the 2s orbital. (Valid)
n=2 l=0 ml=0 ms=-1: This set of quantum numbers is not valid for the spin quantum number ms, which can only have values of +1/2 or -1/2. (Invalid)
From analyzing each option, we can see that there are seven valid sets of quantum numbers listed. It seems like the hint provided is incorrect, as there are more than four valid answers.
There are four electrons, right? So there must be four answers.
#1 electron:
n = 1
l = 0
ml = 0
ms = +1/2
#2 electron:
n = 1
l = 0
ml = 0
ms = -1/2
That's two of them.
#3 electron:
n = 1
l = 0 or 1
ml = etc
All you really need to do is to fill in the blanks as the electrons are added. I've done the two n= 1 electrons, There are now two n = 2 electrons and another hint: l = 0 fills up first.
You're right about the top one and last one not being right.