Instead of principle quantum number (n), azimuthal quantum number (L) &magnetic quantum number m,
a set of new quantum number s, t & u was introduce with similar logic but different value as defined
below
`s=1,2,3,...........oo` all positive integral values.
`t=(s^(2)-1^(1)),(s^(2)-2^(2)),(s^(2)-3^(3))`......... No negative value
`u=((t+1))/2"to"+((t+1))/2`(including zero , if any ) in integral step .
Each orbital can have maximum four electrons .
(s+t) rule is defined ,similar to `(n+l)` rule. The number of subshells in which the third shell is sub divided equal to

Options

A. 1
B. 3
C. 5
D. 7

Explanation

To solve the problem, we need to determine the number of subshells in which the third shell (s = 3) is subdivided using the new quantum numbers defined in the question.

### Step-by-Step Solution:

1. **Identify the value of s**:
- According to the problem, the principal quantum number \( s \) corresponds to the shell number. For the third shell, we have:
\[ s = 3 \]

2. **Calculate the values of t**:
- The values of \( t \) are defined as:
\[ t = s^2 - n^2 \quad \text{for } n = 1, 2, 3, \ldots \]
- For \( s = 3 \):
- For \( n = 1 \):
\[ t = 3^2 - 1^2 = 9 - 1 = 8 \]
- For \( n = 2 \):
\[ t = 3^2 - 2^2 = 9 - 4 = 5 \]
- For \( n = 3 \):
\[ t = 3^2 - 3^2 = 9 - 9 = 0 \]

3. **List the values of t**:
- The calculated values of \( t \) are:
\[ t = 8, 5, 0 \]
- Since \( t \) cannot be negative, we only consider these three values.

4. **Determine the number of subshells**:
- The number of subshells is equal to the number of valid \( t \) values. From our calculations, we have three valid values of \( t \) (8, 5, and 0).
- Therefore, the number of subshells in the third shell is:
\[ \text{Number of subshells} = 3 \]

### Final Answer:
The number of subshells in which the third shell is subdivided is **3**.

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