Step 1: Determine the Molecular Formula

The question asks for isomeric ketones with a molecular weight (MW) of 100. A ketone contains one oxygen atom. A general formula for a saturated acyclic ketone is $C_nH_{2n}O$. The molecular weight is given by: $MW = (12.01 \times n) + (1.008 \times 2n) + 16.00 \approx 12n + 2n + 16 = 14n + 16$ Given MW = 100: $14n + 16 = 100$ $14n = 84$ $n = 6$ So, the molecular formula for the ketones is $C_6H_{12}O$. The degree of unsaturation is $C+1 - H/2 = 6+1-12/2 = 1$, which corresponds to the C=O double bond in a ketone.

Step 2: Identify all Isomeric Ketones (including stereoisomers)

We need to find all structural and stereoisomers of ketones with the formula $C_6H_{12}O$.

1. Hexan-2-one: $CH_3-CO-CH_2-CH_2-CH_2-CH_3$. This molecule is achiral.

2. Hexan-3-one: $CH_3-CH_2-CO-CH_2-CH_2-CH_3$. This molecule is achiral.

3. 3-Methylpentan-2-one: $CH_3-CO-CH(CH_3)-CH_2-CH_3$. The carbon at position 3 (C3) is bonded to four different groups (H, $CH_3$, $C_2H_5$, and $COCH_3$). Thus, C3 is a chiral center. This ketone exists as a pair of enantiomers ((R)- and (S)-3-methylpentan-2-one).

4. 4-Methylpentan-2-one: $CH_3-CO-CH_2-CH(CH_3)_2$. This molecule has no chiral centers and is achiral.

5. 2-Methylpentan-3-one: $CH_3-CH(CH_3)-CO-CH_2-CH_3$. The carbon at position 2 is bonded to H, a $CH_3$ group (C1), another $CH_3$ group (the substituent), and the propionyl group. Since two of the attached groups are identical ($CH_3$), this molecule is achiral.

6. 3,3-Dimethylbutan-2-one (Pinacolone): $CH_3-CO-C(CH_3)_3$. This molecule is achiral.

In total, there are 6 structural isomers. One of them (3-Methylpentan-2-one) is chiral, existing as two stereoisomers. The other 5 are achiral.

Step 3: Analyze the Reaction with $NaBH_4$

The reaction is the reduction of a ketone to a secondary alcohol. $NaBH_4$ provides a hydride ion ($H^-$), which attacks the planar carbonyl carbon. A racemic product (an equimolar mixture of enantiomers) is formed if and only if:

1. The starting material (ketone) is achiral.
2. The reaction creates a new chiral center, resulting in a chiral product (alcohol).

If the starting ketone is already chiral (as a single enantiomer), the product will be a mixture of diastereomers, which is not a racemic mixture. The question specifies that stereoisomers are reacted separately.

Step 4: Evaluate each Isomer's Reaction

Let's analyze the 5 achiral ketones and the 2 chiral stereoisomers.

Achiral Ketones:

1. Hexan-2-one (achiral) $\xrightarrow{NaBH_4}$ Hexan-2-ol Product: $CH_3-CH(OH)-CH_2-CH_2-CH_2-CH_3$. The C2 carbon is bonded to H, OH, $CH_3$, and a butyl group. It is chiral. Since an achiral ketone forms a chiral alcohol, the product is a racemic mixture. (Count = 1)

2. Hexan-3-one (achiral) $\xrightarrow{NaBH_4}$ Hexan-3-ol Product: $CH_3-CH_2-CH(OH)-CH_2-CH_2-CH_3$. The C3 carbon is bonded to H, OH, an ethyl group, and a propyl group. It is chiral. The product is a racemic mixture. (Count = 2)

3. 4-Methylpentan-2-one (achiral) $\xrightarrow{NaBH_4}$ 4-Methylpentan-2-ol Product: $CH_3-CH(OH)-CH_2-CH(CH_3)_2$. The C2 carbon is bonded to H, OH, a methyl group, and an isobutyl group. It is chiral. The product is a racemic mixture. (Count = 3)

4. 2-Methylpentan-3-one (achiral) $\xrightarrow{NaBH_4}$ 2-Methylpentan-3-ol Product: $CH_3-CH(CH_3)-CH(OH)-CH_2-CH_3$. The C3 carbon is bonded to H, OH, an isopropyl group, and an ethyl group. It is chiral. The product is a racemic mixture. (Count = 4)

5. 3,3-Dimethylbutan-2-one (achiral) $\xrightarrow{NaBH_4}$ 3,3-Dimethylbutan-2-ol Product: $CH_3-CH(OH)-C(CH_3)_3$. The C2 carbon is bonded to H, OH, a methyl group, and a tert-butyl group. It is chiral. The product is a racemic mixture. (Count = 5)

Chiral Ketones:

6. (R)- or (S)-3-Methylpentan-2-one (chiral) $\xrightarrow{NaBH_4}$ 3-Methylpentan-2-ol The starting material is a single enantiomer, which is optically active. The product, $CH_3-CH(OH)-CH(CH_3)-CH_2-CH_3$, has two chiral centers (C2 and C3). The reduction creates a new chiral center (C2) in a molecule that already has one (C3). This results in a mixture of diastereomers (e.g., (2R, 3R) and (2S, 3R) from the (3R)-ketone). This product mixture is optically active and is not racemic.

Step 5: Final Count

We have identified 5 ketones that are achiral and upon reduction with $NaBH_4$ yield a chiral alcohol. Each of these reactions produces a racemic mixture.

The total number of ketones that give a racemic product is 5.