Answer:
Following four carbocations are possible from
2-methylbutane, they are given in increasing order of stability.
\[C{{H}_{3}}\to
-\underset{C{{H}_{3}}}{\mathop{\underset{\begin{smallmatrix}
| \\
\uparrow
\end{smallmatrix}}{\mathop{\overset{\beta
}{\mathop{CH}}\,}}\,}}\,\to -\overset{\alpha
}{\mathop{C{{H}_{\begin{smallmatrix}
2 \\
I({{1}^{{}^\circ }})
\end{smallmatrix}}}}}\,-\overset{+}{\mathop{C{{H}_{2}}}}\,<\]
\[\overset{+}{\mathop{C{{H}_{2}}}}\,\to
-\underset{C{{H}_{3}}}{\mathop{\underset{\begin{smallmatrix}
| \\
\uparrow
\end{smallmatrix}}{\mathop{CH}}\,}}\,\to
-\overset{{}}{\mathop{C{{H}_{\begin{smallmatrix}
2 \\
II({{1}^{{}^\circ }})
\end{smallmatrix}}}}}\,-\overset{{}}{\mathop{C{{H}_{3}}}}\,<\]
\[C{{H}_{3}}\to
-\underset{\underset{\text{C}{{\text{H}}_{\text{3}}}}{\mathop{\begin{smallmatrix}
\text{ }\!\!|\!\!\text{ } \\
\uparrow
\end{smallmatrix}}}\,}{\mathop{CH}}\,-\leftarrow
\overset{+}{\mathop{C{{H}_{\begin{smallmatrix}
\\
III({{2}^{{}^\circ }})
\end{smallmatrix}}}}}\,-\leftarrow
C{{H}_{3}}<\]
\[C{{H}_{3}}\to
-\underset{\underset{\text{C}{{\text{H}}_{\text{3}}}}{\mathop{\begin{smallmatrix}
\text{ }\!\!|\!\!\text{ } \\
\uparrow
\end{smallmatrix}}}\,}{\mathop{\overset{+}{\mathop{C}}\,}}\,-\leftarrow
C{{H}_{\begin{smallmatrix}
2 \\
IV({{3}^{{}^\circ }})
\end{smallmatrix}}}-\leftarrow
C{{H}_{3}}\]
The stability of carbocation
decreases in the order\[3{}^\circ \text{ }>\text{ }2{}^\circ \text{
}>\text{ }1{}^\circ \]. Out of the two \[1{}^\circ \]carbocations, (II)
carbocation has an electron donating \[C{{H}_{3}}\] group at \[\alpha \]-carbon
while carbocation\[(I)\]has a \[C{{H}_{3}}\] group at \[\beta \]-carbon. Since,
\[+I\] effect decreases with distance, therefore carbocation (II) is more
stable than carbocation (I).
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