2
Step 1: Understanding Isomerism
Isomers are compounds with the same molecular formula but different structural arrangements or spatial orientations. The molecular formula given is \( C_4H_9Br \), which corresponds to butyl bromide isomers.
Step 2: Identifying the Isomers
The possible structural and stereoisomers for \( C_4H_9Br \) are:
1. n-Butyl bromide (\( CH_3CH_2CH_2CH_2Br \)) - Straight-chain structure.
2. Isobutyl bromide (\( (CH_3)_2CHCH_2Br \)) - Branched structure.
3. Sec-butyl bromide (\( CH_3CHBrCH_2CH_3 \)) - Branched with a secondary carbon.
4. Tert-butyl bromide (\( (CH_3)_3CBr \)) - Branched with a tertiary carbon.
5. Sec-butyl bromide has a chiral center, leading to two enantiomers, contributing to stereoisomerism.
Step 3: Evaluating the Given Options
- Option (1) 3: Incorrect, as it does not account for all possible isomers.
- Option (2) 4: Incorrect, as it excludes stereoisomers.
- Option (3) 5: Correct, as it includes all structural and stereoisomers.
- Option (4) 2: Incorrect, as more isomers exist.
Thus, the correct answer is
Option (3).
In Bohr model of hydrogen atom, if the difference between the radii of \( n^{th} \) and\( (n+1)^{th} \)orbits is equal to the radius of the \( (n-1)^{th} \) orbit, then the value of \( n \) is:
Given the function:
\[ f(x) = \frac{2x - 3}{3x - 2} \]
and if \( f_n(x) = (f \circ f \circ \ldots \circ f)(x) \) is applied \( n \) times, find \( f_{32}(x) \).
For \( n \in \mathbb{N} \), the largest positive integer that divides \( 81^n + 20n - 1 \) is \( k \). If \( S \) is the sum of all positive divisors of \( k \), then find \( S - k \).
If the real-valued function
\[ f(x) = \sin^{-1}(x^2 - 1) - 3\log_3(3^x - 2) \]is not defined for all \( x \in (-\infty, a] \cup (b, \infty) \), then what is \( 3^a + b^2 \)?