Step 1: Identify the reaction type.
The reagent used is
\[
Na/\text{dry ether}
\]
which indicates the
Wurtz reaction.
In a Wurtz reaction, two molecules of an alkyl halide couple together:
\[
2R-X + 2Na \rightarrow R-R + 2NaX
\]
Step 2: Analyze the product formed.
The product is
\[
(CH_3)_2CHCH_2CH_2CH(CH_3)_2
\]
This can be written as
\[
(CH_3)_2CH-CH_2-CH_2-CH(CH_3)_2
\]
The molecule is symmetrical about the central
\[
-CH_2-CH_2-
\]
unit.
Step 3: Split the product into two identical halves.
Breaking the central carbon-carbon bond gives
\[
(CH_3)_2CHCH_2-
\]
and
\[
-CH_2CH(CH_3)_2
\]
Thus, each alkyl fragment is
\[
(CH_3)_2CHCH_2-
\]
which is the
isobutyl group.
Step 4: Determine the corresponding alkyl halide.
The alkyl halide that produces the isobutyl group is
\[
(CH_3)_2CHCH_2Br
\]
whose IUPAC name is
1-Bromo-2-methylpropane
On Wurtz coupling:
\[
2(CH_3)_2CHCH_2Br
\xrightarrow[dry\ ether]{2Na}
(CH_3)_2CHCH_2CH_2CH(CH_3)_2
+2NaBr
\]
which matches the given product.
Step 5: Final conclusion.
Therefore, the starting compound \(P\) is
\[
\boxed{\text{1-Bromo-2-methylpropane}}
\]
Hence, option (1) is correct.