Arrange the following in the decreasing order of their melting points:
I. Decane II. Nonane
III. Octane IV. Heptane

Options

A. (a) `(I) gt (II) gt (III) gt (IV)`
B. (b) `(IV) gt (III) gt (II) gt (I)`
C. (c) `(I) gt (III) gt (II) gt (IV)`
D. (d) `(IV) gt (II) gt (III) gt (I)`

Explanation

To arrange the given alkanes in decreasing order of their melting points, we will follow these steps:

### Step 1: Identify the Molecular Formulas
We start by identifying the molecular formulas of the alkanes given in the question:
- Decane: C₁₀H₂₂
- Nonane: C₉H₂₀
- Octane: C₈H₁₈
- Heptane: C₇H₁₆

### Step 2: Understand the Melting Point Trends
Next, we need to understand the trends in melting points for alkanes. The melting points of alkanes generally increase with an increase in the number of carbon atoms. However, there is an important distinction:
- Alkanes with an even number of carbon atoms tend to have higher melting points than those with an odd number of carbon atoms. This is due to the "packing effect," where even-numbered alkanes can pack more closely in a solid state.

### Step 3: Compare the Alkanes
Now, we will compare the alkanes based on the number of carbon atoms:
- Decane (C₁₀H₂₂) - Even number of carbons
- Nonane (C₉H₂₀) - Odd number of carbons
- Octane (C₈H₁₈) - Even number of carbons
- Heptane (C₇H₁₆) - Odd number of carbons

### Step 4: Arrange in Decreasing Order
Based on the trends and the number of carbon atoms:
1. Decane (C₁₀H₂₂) - Highest melting point (even number)
2. Octane (C₈H₁₈) - Second highest melting point (even number)
3. Nonane (C₉H₂₀) - Third highest melting point (odd number)
4. Heptane (C₇H₁₆) - Lowest melting point (odd number)

### Final Order
Thus, the decreasing order of melting points is:
**Decane > Octane > Nonane > Heptane**