Question

Which of the following electron quantum number designations is impossible? Order is n,l,m,s

• 2.0,1.1/2
• 3,0,0, 1/2
• 4,2-1,1/2
• 6,5.4.1/2

Answer 1

Step 1: Explanation:

In atoms, there are a total of four quantum numbers: the principal quantum number (n), the orbital angular momentum quantum number (l), the magnetic quantum number (ml), and the electron spin quantum number (ms).

The Principal Quantum Number (n): The principal quantum number ( n) designates the principal electron shell.It can be any positive integer starting at 1.( i.e n=1,2,3,4) as n=1 designates the first principal shell (the innermost shell).

The Orbital Angular Momentum Quantum Number (l):

The orbital angular momentum quantum number l determines the shape of an orbital.The value of l can be zero. It can also be a positive integer, it always one less than the principal quantum number (n-1).

i.e l =0,1,2,3.....(n-1)

The Magnetic Quantum Number (ml):

The magnetic quantum number (ml) determines the number of orbitals and their orientation within a subshell. Consequently, its value depends on the orbital angular momentum quantum number (l). Given a certain value of l, the (ml) is an interval ranging from ( -l to +l ).

The Electron Spin Quantum Number (Ms):

It designates the direction of the electron spin and may have a spin of +1/2, represented by↑, or –1/2, represented by ↓.

Step 2: solution

(a)

Given,

(n,l,m,s) = (2,0,1,1/2)

since we know for a given value of n, the value of l must be 0 to n-1

if n = 2 then ,the possible value of l = 0,1

but the given set contains l =0

so if l = 0 then the value of m is only 0 since we know for a given value of l , the value of m must be -l to +l

but in given set m = 1 is given which is not possible hence, the given set of quatum number is impossible

(b)

Given,

(n,l,m,s) = (3,0,0,-1/2)

if n = 3 then ,the possible value of l = 0,1,2

but the given set contains l =0

so if l = 0 then the value of m is only 0 and s can be either 1/2 or -1/2 hence the given set of quatum number is possible

(c)

Given,

(n,l,m,s) = (4,2,-1,1/2)

if n = 4 then ,the possible value of l = 0,1,2,3

but the given set contains l = 2

so if l = 2 then the value of m is can either -2,-1,0,1,2 and s can be either 1/2 or -1/2 hence the given set of quatum number is possible

(d)

Given,

(n,l,m,s) = (6,5,4,1/2)

if n = 6 then ,the possible value of l = 0,1,2,3,4,5

but the given set contains l = 5

so if l = 5 then the value of m is can either -5,-4,-3,-2,-1,0,1,2 ,3,4,5 and s can be either 1/2 or -1/2 hence the given set of quatum number is possible

hence, the option(a) is not possible