When the quantity of a radioactive substance is increased two times, the number of atoms disintegrating per unit time is

Options

A. Doubled
B. Increased by square of two
C. Increased but not a great extent
D. Not affected

Answer

To solve the problem, we need to understand the relationship between the quantity of a radioactive substance and the number of atoms disintegrating per unit time.

### Step-by-Step Solution:

1. **Understanding Radioactive Decay**:
Radioactive decay follows first-order kinetics, which means the rate of decay is directly proportional to the number of radioactive atoms present.

2. **Defining the Rate of Disintegration**:
The rate of disintegration can be expressed mathematically as:
\[ -\frac{dN}{dt} = \lambda N \]
where:
- \( \frac{dN}{dt} \) is the rate of disintegration (number of atoms disintegrating per unit time),
- \( \lambda \) is the decay constant,
- \( N \) is the number of radioactive atoms present.

3. **Doubling the Quantity of the Substance**:
If the quantity of the radioactive substance is increased two times, we can denote the new quantity as \( N' = 2N \).

4. **Calculating the New Rate of Disintegration**:
Substituting \( N' \) into the rate equation gives:
\[ -\frac{dN'}{dt} = \lambda N' = \lambda (2N) = 2\lambda N \]
This shows that the new rate of disintegration \( -\frac{dN'}{dt} \) is twice the original rate.

5. **Conclusion**:
Therefore, when the quantity of the radioactive substance is increased two times, the number of atoms disintegrating per unit time is doubled.

### Final Answer:
The number of atoms disintegrating per unit time is doubled.

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