If `3//4` quantity of a radioactive element disintegrates in two hours, its half life would be

Options

A. 1 hours
B. 45m
C. 30m
D. 15m

Answer

To find the half-life of a radioactive element when 3/4 of its quantity disintegrates in 2 hours, we can follow these steps:

### Step 1: Understand the Disintegration
If 3/4 of the radioactive element disintegrates, this means that only 1/4 of the original quantity remains.

### Step 2: Relate Disintegration to Half-Life
The half-life is defined as the time required for half of the radioactive substance to disintegrate. In this case, we need to determine how many half-lives it takes for the quantity to reduce from the original amount to 1/4 of its original quantity.

### Step 3: Calculate the Number of Half-Lives
1. After the first half-life, 1/2 of the original quantity remains.
2. After the second half-life, 1/2 of the remaining quantity (which is 1/2 of the original) will remain, which is (1/2) * (1/2) = 1/4 of the original quantity.

This means that it takes 2 half-lives for the quantity to reduce to 1/4.

### Step 4: Determine the Total Time for 2 Half-Lives
We know from the problem statement that the total time taken for 3/4 of the quantity to disintegrate (leaving 1/4 remaining) is 2 hours.

### Step 5: Calculate the Half-Life
Since it takes 2 half-lives to reach 1/4 of the original quantity, we can find the half-life by dividing the total time by the number of half-lives:
\[ \text{Half-life} = \frac{\text{Total time}}{\text{Number of half-lives}} = \frac{2 \text{ hours}}{2} = 1 \text{ hour} \]

### Final Answer
The half-life of the radioactive element is **1 hour**.

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