11.
(a)
(i) Heisenberg uncertainty principle states that, “It is impossible to determine both the position and momentum of electron simultaneously with greater accuracy.”
(a)
(i) Heisenberg uncertainty principle states that, “It is impossible to determine both the position and momentum of electron simultaneously with greater accuracy.”
(ii) Hund's rule, states that, "When more than one orbital of equal energies are present, then the electrons first occupy
(iii) Pauli’s Principle states that
“No two electrons in an atom can have the same values for all the four quantum numbers”
(iv) According to Aufbau's principle "The electrons in an atom are so arranged that they occupy orbitals in the order of their increasing energies."
(b) The following sets of quantum numbers are NOT allowed in hydrogen atom:
(i) n = 1, L = 1, ml = 0
The value of L usually is =n-1. So for n=1, L must be 0. Which means only 1 sub shell is present in the first shell(n) which(the sub-shell,L) is denoted by 0=S-sub-shell.
For that reason we cannot have such a serial quantum number in H atom with the principle quantum number of n=1 with two sub-shells( i.e L=1). Because, Only there is L=0 for n=1 in H atom.
(ii) n = 1, L = 0, ml = 2
In an atom for n=1 shell, L=0 s,sub-shell, but ml,magnetic quantum number shows number of orbitals, which in this case has to be only 1 orbital which is "s" but instead it indicates ml=2 which is not possible.
That reason it's impossible to have ml=2 for n=1 or L=0.
(iii) n = 4, L = 3, ml = 4
For n=4 and L=3
The reader should remember this ml=n^2( the square of n gives ml, number of orbitals for a given number of shells).
so ml=4^2. which must be ml=16 not 4. for this reason it's impossible for an atom to have n=4, L=3 with ml=16.
(iv) n = 0, L = 0, ml = 0.
Precisely n=0 means no shells at all,shells and no atom, (so without shells i.e. n=0, how can we possibly have a sub-shell ml=0 ?) in other words for L=0, there has to be n=1 not n=0. so for this reason it's impossible to have an atom with n=0, L=0 with ml=0.
(v) n = 2, L = -1, ml = 1
As n=2, for L=n-1
.: L≠-1 but L=1 not to mention ml=n² which should be 4.
The reader should remember that L must be a whole positive counting number or 0(zero).
this tells an atom within=2, will have L=1 and ml=4 not other the other way.
(c)
(i) In 1s sub-shell only is there a single orbital, i.e. ml=1.
(ii) In 2p sub-shell, there are three orbitals, i.e. ml=3.
(iii) A 3d sub-shell, has five orbitals, i.e ml=5.
(iv) For 4f sub-shell, has seven orbitals, i.e. ml=7
d)
(i) Mind that, K is a traditional name for principal quantum number n=1.
And sub-level stands for sub-shells or Azimuthal quantum number(L),
Since, L=n-1
then for n=1, L=0 whose value indicate 1 sub-shell, so we only have 1 sub-level for a K shell.
(ii) N stands for a modern principal quantum number n=4, as L=n-1. thus L=3, i.e 0-s, 1-p, 2-d and 3-d sub-levels.
.: for N shell has four(4) sub-shells.
(iii) L represents a principal quantum number n=2,
recall; the value of L=n-1 then, L=1, i.e. 0-s and 1-p sub-levels.
Frankly speaking, L shell has two(2) sub-shells.
(e)
(i) This is a correct configuration of electron in the orbital as far as it obeys the Hund's rule of maximum multiplicity.
(ii) This is an incorrect arrangement of electrons as does not obey the Pauli's exclusion principle, i.e. the "s" sub-level is not yet fully filled with electrons and it's lower in energy compared to its neighbour "p" sub-shell, there's no way ordinary electrons will occupy any of its orbitals before "s" is fully filled.
(iii) This is not the correct order to fill electrons in an atom according to the "Hund's rule" as the degenerate orbitals are present to fill with electrons no pairing is allowed except for each of the degenerate orbitals has at least one electron.
In the case above the "pz" orbital must also be occupied by a single electron then pairing can begin not the other way around so the order violated the Hund's rule.
(iv) Same applies here for pairing of electrons only shall be observed as each of the "p" orbitals are singly occupied as long as the "pz" orbital is all way empty, there's no way pairing can be issued not to mention pairing also follows the pauli's exclusion principle from left to right i.e. px<py<pz.
these orbitals separately with parallel spins. The pairing of electrons will only be after all the orbitals of a given sub-energy level are singly occupied."
(iii) Pauli’s Principle states that
“No two electrons in an atom can have the same values for all the four quantum numbers”
(iv) According to Aufbau's principle "The electrons in an atom are so arranged that they occupy orbitals in the order of their increasing energies."
(b) The following sets of quantum numbers are NOT allowed in hydrogen atom:
(i) n = 1, L = 1, ml = 0
The value of L usually is =n-1. So for n=1, L must be 0. Which means only 1 sub shell is present in the first shell(n) which(the sub-shell,L) is denoted by 0=S-sub-shell.
For that reason we cannot have such a serial quantum number in H atom with the principle quantum number of n=1 with two sub-shells( i.e L=1). Because, Only there is L=0 for n=1 in H atom.
(ii) n = 1, L = 0, ml = 2
In an atom for n=1 shell, L=0 s,sub-shell, but ml,magnetic quantum number shows number of orbitals, which in this case has to be only 1 orbital which is "s" but instead it indicates ml=2 which is not possible.
That reason it's impossible to have ml=2 for n=1 or L=0.
(iii) n = 4, L = 3, ml = 4
For n=4 and L=3
The reader should remember this ml=n^2( the square of n gives ml, number of orbitals for a given number of shells).
so ml=4^2. which must be ml=16 not 4. for this reason it's impossible for an atom to have n=4, L=3 with ml=16.
(iv) n = 0, L = 0, ml = 0.
Precisely n=0 means no shells at all,shells and no atom, (so without shells i.e. n=0, how can we possibly have a sub-shell ml=0 ?) in other words for L=0, there has to be n=1 not n=0. so for this reason it's impossible to have an atom with n=0, L=0 with ml=0.
(v) n = 2, L = -1, ml = 1
As n=2, for L=n-1
.: L≠-1 but L=1 not to mention ml=n² which should be 4.
The reader should remember that L must be a whole positive counting number or 0(zero).
this tells an atom within=2, will have L=1 and ml=4 not other the other way.
(c)
(i) In 1s sub-shell only is there a single orbital, i.e. ml=1.
(ii) In 2p sub-shell, there are three orbitals, i.e. ml=3.
(iii) A 3d sub-shell, has five orbitals, i.e ml=5.
(iv) For 4f sub-shell, has seven orbitals, i.e. ml=7
d)
(i) Mind that, K is a traditional name for principal quantum number n=1.
And sub-level stands for sub-shells or Azimuthal quantum number(L),
Since, L=n-1
then for n=1, L=0 whose value indicate 1 sub-shell, so we only have 1 sub-level for a K shell.
(ii) N stands for a modern principal quantum number n=4, as L=n-1. thus L=3, i.e 0-s, 1-p, 2-d and 3-d sub-levels.
.: for N shell has four(4) sub-shells.
(iii) L represents a principal quantum number n=2,
recall; the value of L=n-1 then, L=1, i.e. 0-s and 1-p sub-levels.
Frankly speaking, L shell has two(2) sub-shells.
(e)
(i) This is a correct configuration of electron in the orbital as far as it obeys the Hund's rule of maximum multiplicity.
(ii) This is an incorrect arrangement of electrons as does not obey the Pauli's exclusion principle, i.e. the "s" sub-level is not yet fully filled with electrons and it's lower in energy compared to its neighbour "p" sub-shell, there's no way ordinary electrons will occupy any of its orbitals before "s" is fully filled.
(iii) This is not the correct order to fill electrons in an atom according to the "Hund's rule" as the degenerate orbitals are present to fill with electrons no pairing is allowed except for each of the degenerate orbitals has at least one electron.
In the case above the "pz" orbital must also be occupied by a single electron then pairing can begin not the other way around so the order violated the Hund's rule.
(iv) Same applies here for pairing of electrons only shall be observed as each of the "p" orbitals are singly occupied as long as the "pz" orbital is all way empty, there's no way pairing can be issued not to mention pairing also follows the pauli's exclusion principle from left to right i.e. px<py<pz.
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