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### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# 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 ${{\mathbit{m}}}_{{\mathbf{l}}}$ 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 ${{\mathbit{m}}}_{{\mathbf{l}}}{\mathbf{=}}{\mathbf{0}}$ . (f) There are n sub shells for each value of n .

1. The given statement is true.
2. The given statement is true.
3. The given statement is true.
4. The given statement is true.
5. The given statement is true.
6. The given statement is true.
See the step by step solution

## Step 1: The given data

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

## Step 2: Understanding the concept of the electronic configuration

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.

## Step 3: a) Calculation of not possible state configuration

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.

## Step 4: b) Calculation of the dependence of the magnetic quantum number

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

## Step 5: c) Calculation of the number of sub shells for n = 4

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.

## Step 6: d) Calculation of the smallest value of n

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.

## Step 7: e) Calculation of the values of magnetic quantum number for l = 0

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.

## Step 8: f) Calculation of the number of sub shells for n

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.