Arrangements of `(CH_(3))_(3)C-,(CH_(3))_(2)CH-,CH_(3).CH_(2)-` when attached to benzyl or `n` unsaturated group in increasing order of inductive effects is:

Options

A. `(CH_(3))_(3)C^(-) lt (CH_(3))_(2)CH^(-) lt (CH_(3)).CH_(2)`
B. `CH_(3).CH_(2)^(-) lt (CH_(3))_(2)CH^(-) lt (CH_(3))_(3)C^(-)`
C. `(CH_(3))_(2)CH^(-) lt (CH_(3))_(3)C^(-) lt CH_(3).CH_(2)^(-)`
D. `(CH_(3))_(3)C^(-) lt CH_(3).CH_(2)^(-) lt (CH_(3))_(2)CH^(-)`

Explanation

To determine the increasing order of inductive effects for the groups `(CH₃)₃C-`, `(CH₃)₂CH-`, and `CH₃CH₂-` when attached to a benzyl or an unsaturated group, we can analyze the groups based on their ability to donate electron density through the inductive effect.

### Step-by-step Solution:

1. **Identify the Groups**: We have three groups to consider:
- `(CH₃)₃C-` (tert-butyl group)
- `(CH₃)₂CH-` (isopropyl group)
- `CH₃CH₂-` (ethyl group)

2. **Understand Inductive Effect**: The inductive effect refers to the electron-donating or withdrawing effect of substituents through sigma bonds. Groups that can donate electrons will have a positive inductive effect (+I), while groups that withdraw electrons will have a negative inductive effect (-I).

3. **Evaluate Each Group**:
- **(CH₃)₃C-**: This group has three methyl groups. The presence of multiple methyl groups increases the electron density through hyperconjugation and inductive effects, making it a strong electron-donating group.
- **(CH₃)₂CH-**: This group has two methyl groups. It also donates electron density but to a lesser extent than the tert-butyl group.
- **CH₃CH₂-**: This group has one methyl group and is the weakest in terms of inductive effect among the three groups.

4. **Rank the Groups**: Based on the number of methyl groups and their ability to donate electron density, we can rank the groups in increasing order of their inductive effects:
- `CH₃CH₂-` (weakest inductive effect)
- `(CH₃)₂CH-` (moderate inductive effect)
- `(CH₃)₃C-` (strongest inductive effect)

5. **Final Arrangement**: Therefore, the increasing order of inductive effects when attached to benzyl or an unsaturated group is:
- `CH₃CH₂- < (CH₃)₂CH- < (CH₃)₃C-`