Label these statements as true or false:

(a) One (and only one) of these sub shells cannot exist: 2p,4f,3d,1p

(b) The number of values of${\mathit{m}}_{\mathbf{l}}$ that are allowed depends on l and not on n.

(c) There are four sub shells for n = 4 .

(d) The smallest value of for a given value of l is l + 1 .

(e) All states with l = 0 also have${\mathit{m}}_{\mathbf{l}}\mathbf{=}\mathbf{0}$ .

(f) There are n sub shells for each value of n .

There are different electronic configuration statements that need to be verified.

The electronic configuration with the principal quantum number, n, has an orbital angular quantum number in the range of 0 to n-1 integer values.

In contrast, the range of magnetic angular quantum number ranges from -l to +l. The number of sub-shells is equal to the principal quantum number.

From any principal quantum number, we can get the number of the sub-shells in that electronic configuration that is s, p, d, and f.

So, here the state is not possible as the orbital quantum number of this state is l = 1(for p) . This is equal to the principal quantum number (n = 1), which is impossible.

Hence, this statement is true.

The value of magnetic quantum number$m_l$ ranges from -l to +l . Thus, it depends on the value of l , not on the value of n .

Hence, this statement is true

The number of sub-shells of an orbital is equal to the principal number.

Thus, the number of sub shells for n = 4 is 4.

Hence, this statement is true.

We know that the values of orbital quantum numbers l range from 0 to (n-1).

Thus, here the smallest value of for any value of is given by:

l = n -1

n = l + 1

Hence, this statement is true.

We know that the values of magnetic quantum number for any value of range from -l to +l . Thus, for the value l = 0 , the only value of$m_l$ is$m_l=0$ .

Hence, this statement is true.

From the concept, we can say that the number of sub-shells of an orbital is equal to its principal quantum number n .

Hence, this statement is true.