The mass average molecular mass & number average molecular mass of a polymer are 40,000 and 30,000 respectively. The polydispersity index of polymer will be

Options

A. `lt1`
B. `gt1`
C. 1
D. 0

Explanation

To find the polydispersity index (PDI) of a polymer, we can use the following formula:

\[ \text{Polydispersity Index (PDI)} = \frac{\text{Mass Average Molecular Mass}}{\text{Number Average Molecular Mass}} \]

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass Average Molecular Mass (M_m) = 40,000
- Number Average Molecular Mass (M_n) = 30,000

2. **Substitute the values into the formula:**
\[ \text{PDI} = \frac{M_m}{M_n} = \frac{40,000}{30,000} \]

3. **Perform the division:**
\[ \text{PDI} = \frac{40,000}{30,000} = \frac{4}{3} \approx 1.33 \]

4. **Interpret the result:**
The polydispersity index (PDI) is approximately 1.33. This indicates that the polymer has a distribution of molecular weights, and since the PDI is greater than 1, it confirms that there is some degree of polydispersity in the polymer sample.

### Final Answer:
The polydispersity index of the polymer is approximately **1.33**.

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