If 5g of a radioactive substance has a `t_((1)/(2))=14h`, 20g of the same substance will have a `t_((1)/(2))` equal to

Options

A. 56h
B. 3.5h
C. 14h
D. 28h

Answer

To solve the question regarding the half-life of a radioactive substance, we need to understand the concept of half-life and how it relates to the amount of substance present.

### Step-by-Step Solution:

1. **Understanding Half-Life**: The half-life (t₁/₂) of a radioactive substance is the time required for half of the radioactive atoms in a sample to decay. It is a characteristic property of the substance and does not depend on the amount of the substance present.

2. **Given Data**: We are given that 5g of a radioactive substance has a half-life (t₁/₂) of 14 hours.

3. **Analyzing the Question**: The question asks for the half-life of 20g of the same substance. Since half-life is a property that does not depend on the quantity of the substance, the half-life for any amount of the same radioactive substance remains constant.

4. **Conclusion**: Therefore, the half-life of 20g of the radioactive substance will also be 14 hours.

### Final Answer:
The half-life (t₁/₂) of 20g of the same radioactive substance is **14 hours**.

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