For each electron in a ground-state Be atom, select the set of quantum numbers that represents it. Check all that apply.
( ) n=2, l=0, ml=0, ms=+1/2
( ) n=1, l=0, ml=0, ms=+1/2
( ) n=2, l=1, ml=0, ms=-1/2
( ) n=2, l=1, ml=1, ms=+1/2
( ) n=2, l=0, ml=0, ms=-1
( ) n=2, l=0, ml=0, ms=-1/2
( ) n=1, l=0, ml=-1, ms=+1/2
( ) n=1, l=0, ml=0, ms=-1/2
Thanks.
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To determine the set of quantum numbers that represents an electron in a ground-state Be atom, we need to consider the following rules:
1. The principal quantum number (n) represents the energy level of the electron and can have integer values starting from 1.
2. The azimuthal quantum number (l) represents the shape of the orbital and can have integer values from 0 to (n-1).
3. The magnetic quantum number (ml) represents the orientation of the orbital and can have integer values from -l to +l.
4. The spin quantum number (ms) represents the direction of the electron's spin and is either +1/2 (spin-up) or -1/2 (spin-down).
Now, let's go through each option and check if it satisfies the conditions:
( ) n=2, l=0, ml=0, ms=+1/2: This set of quantum numbers is valid. The principal quantum number (n) is 2, the azimuthal quantum number (l) is 0, the magnetic quantum number (ml) is 0, and the spin quantum number (ms) is +1/2.
( ) n=1, l=0, ml=0, ms=+1/2: This set of quantum numbers is invalid. According to the rules, the azimuthal quantum number (l) should be less than the principal quantum number (n-1). In this case, n=1 and l=0 violates this condition.
( ) n=2, l=1, ml=0, ms=-1/2: This set of quantum numbers is valid. The principal quantum number (n) is 2, the azimuthal quantum number (l) is 1, the magnetic quantum number (ml) is 0, and the spin quantum number (ms) is -1/2.
( ) n=2, l=1, ml=1, ms=+1/2: This set of quantum numbers is invalid. The magnetic quantum number (ml) cannot be greater than the azimuthal quantum number (l). In this case, ml=1 exceeds l=1.
( ) n=2, l=0, ml=0, ms=-1: This set of quantum numbers is invalid. The spin quantum number (ms) can only be +1/2 or -1/2.
( ) n=2, l=0, ml=0, ms=-1/2: This set of quantum numbers is valid. The principal quantum number (n) is 2, the azimuthal quantum number (l) is 0, the magnetic quantum number (ml) is 0, and the spin quantum number (ms) is -1/2.
( ) n=1, l=0, ml=-1, ms=+1/2: This set of quantum numbers is invalid. The magnetic quantum number (ml) should satisfy -l <= ml <= l. In this case, l=0 and ml=-1 violates this condition.
( ) n=1, l=0, ml=0, ms=-1/2: This set of quantum numbers is valid. The principal quantum number (n) is 1, the azimuthal quantum number (l) is 0, the magnetic quantum number (ml) is 0, and the spin quantum number (ms) is -1/2.
Therefore, the correct sets of quantum numbers that represent electrons in a ground-state Be atom are:
- n=2, l=0, ml=0, ms=+1/2
- n=2, l=1, ml=0, ms=-1/2
- n=2, l=0, ml=0, ms=-1/2
- n=1, l=0, ml=0, ms=-1/2
You have 4 electrons in Be. The configuration is 1s2 2s2.
For the two outside electrons n = 2, s electrons have l = 0 so you are looking at
n = 2, l=0, ms = +1/2 and -1/2
You do the two inside electrons the same way but of course n = 1.