how many subshells are possible if arbitrary period number (10) is established
Answers
Answer:
Well, this is kind of open to interpretation... but if I interpreted it correctly, I get
27
elements, compared to the original
18
elements, in the 4th period of the periodic table.
(If you already knew that the number of electrons allowed in a given orbital is derived from the properties of electrons, and NOT of the orbitals themselves, the answer quickly follows.)
PRELIMINARY THINGS
I think there's a typo in the question... I looked this up elsewhere, and it's probably...
If each orbital can hold a maximum of 3 electrons, the number of elements in the 4th period of the periodic table (long form) is...?
Also, note that this is entirely theoretical, as all electrons only have two possible spins (
m
s
=
±
1
2
) in a given orbital, and no two electrons can share the same quantum state (Pauli Exclusion Principle); that restricts each orbital to contain only two electrons in real life.
That aside, when we suppose three electrons are "allowed" in a single orbital (assuming the other three quantum numbers are as normal), we suddenly "allow"
50
%
more elements in a given quantum level.
(It's not really why the periodic table was arranged historically, but... I suppose that's what the intent of this question was...)
EXPANDING THE PERIOD...
An electron configuration for the fourth period in a generalized manner is written as:
4
s
x
3
d
x
4
p
x
where:
x
=
(
2
l
+
1
)
⋅
N
m
s
is the total number of electrons in all the orbitals in a given subshell.
l
is the angular momentum quantum number.
l
=
0
,
1
,
2
,
3
,
.
.
.
corresponds to
s
,
p
,
d
,
f
,
.
.
.
orbitals.
2
l
+
1
is known as the degeneracy of the subshell; it is how many orbitals are in that subshell.
N
m
s
is an arbitrary number of spins the electron could have, as it also then gives the maximum number of electrons per orbital. In this case we SUPPOSE that
N
m
s
=
3
, but in real life it is just
2
.
Now, the number of allowed
m
s
values derives from the properties of the electron, not of the orbitals themselves, so having more spins allowed does NOT change the orbital shapes or relative energies.
For the
4
s
orbital:
l
=
0
,
⇒
2
l
+
1
=
1
For the
3
d
orbitals:
l
=
2
,
⇒
2
l
+
1
=
5
For the
4
p
orbitals:
l
=
1
,
⇒
2
l
+
1
=
3
Thus, the hypothetical electron configuration we would then write is...
4
s
1
⋅
3
3
d
5
⋅
3
4
p
3
⋅
3
=
4
s
3
3
d
15
4
p
9
And that would apparently expand the fourth period of the periodic table from
18
elements to
27
elements.