Question 2.67 (a) How many sub-shells are associated with n = 4?
(b) How many electrons will be present in the sub-shells having ms value of –1/2 for n = 4?
Class XI Structure of Atom Page 69
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(a) n = 4 { principal quantum number = 4 }
now, azimuthal quantum number {l} = 0, 1, 2, 3
if l = 0, then, subshell is 's'
if l = 1 then, subshell is 'p'
if l = 2 then, subshell is 'd'
if l = 3 then, subshell is 'f'
hence, number of subshell = 4
(b) if n = 4
maximum number of orbitals present in nth subshell = n²
so, number of electrons = (4)² = 16
but we know, The maximum number of electrons present in any orbital is two and each orbital has one electron with negative spin ms = -1/2 and one electron with positive spin ms = +1/2 . Hence, there are 16 electrons with ms = -1/2
now, azimuthal quantum number {l} = 0, 1, 2, 3
if l = 0, then, subshell is 's'
if l = 1 then, subshell is 'p'
if l = 2 then, subshell is 'd'
if l = 3 then, subshell is 'f'
hence, number of subshell = 4
(b) if n = 4
maximum number of orbitals present in nth subshell = n²
so, number of electrons = (4)² = 16
but we know, The maximum number of electrons present in any orbital is two and each orbital has one electron with negative spin ms = -1/2 and one electron with positive spin ms = +1/2 . Hence, there are 16 electrons with ms = -1/2
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