Question

Missed a lecture due to illness and am struggling with these, help is super appreciated!

(a) The quantum number n describes____ the of an atomic orbital and the quantum number l describes its____

(b) When n = 4, the possible values of l are:

c) What type of orbital corresponds to l = 0?

(d) What type of atomic orbital has 0 nodal planes?

(e) The maximum number of orbitals that may be associated with the quantum number set n = 1, l = 0, and ml = 0 is?

(f) How many subshells are in the n = 2 shell?

(g) How many orbitals are in the n = 4 shell?

(h) How many orbitals are in the l = 3 subshell?

(i) The maximum number of orbitals that may be associated with the quantum numbers n = 3 and l = 0 is

Answer 1

a) The quantum number n describes the size of an atomic orbital and the quantum number l describes its shape.

b) The quantum number l can have any integer between 0 and n-1.

If n = 4,

n-1 = 4-1 =3

So, l can have values between 0 and 3. It can have 0,1,2 or 3 as its value.

c. If the value of l is equal to 0, it will have s orbital which is spherical in shape.

l = 0 corresponds to s orbital.

If l = 1, the orbital will be p orbital.

If l = 2, the orbital will be d orbital.

d Ans.

s atomic orbitals do not have nodal planes since they are speherical. However, they have radial nodes (except 1s orbital).

e. Here, the principal quantum no., n = 1

Azimuthal quantum no., l = 0

l = 0 means that it is an s orbital. The given quantum no. set signifies 1 orbital, that is, 1s.

f. If n= 2 shell, the no. of sub shells = 2

The shell no. is equal to the no. of subshells possible.

For n= 2 shell, the two sub shells are 2s and 2p.

g. For n = 4 shell, the subshells are

1. 4s (which has 1 orbital)

2. 4p (which has 3 orbitals)

3. 4d ( which has 5 orbitals)

4. 4f (which has 7 orbitals)

So, total no. of orbitals = 1 + 3 + 5 + 7 = 16 orbitals

Therefore, there are 16 orbitals in n = 4 shell.

h. If l = 0, it is s subshell

If l = 1, it is p subshell

If l = 2, it is d subshell

Here, l = 3, this indicates it is an f sub shell.

f subshell has 7 orbitals.

Therefore, there are 7 orbitals in l = 3 subshell.

i. Here, n = 3 and l = 0.

The quantum numbers indicate it is 3s orbital.

s has only one orbital.

So, the maximum no. of orbital associated with the quantum no. is only one.