Which among the following relations is correct?
(a)`t_(3//4) = 2t_(1//2)`
(b)`t_(3//4) = 3t_(1//2)`
(c)`t_(3//4) = 1/2t_(1//2)`
(d)`t_(3//4) = 1/3t_(1//2)`

Options

A. a)`t_(3//4) = 2t_(1//2)`
B. b)`t_(3//4) = 3t_(1//2)`
C. c)`t_(3//4) = 1/2t_(1//2)`
D. d)`t_(3//4) = 1/3t_(1//2)`

Explanation

To solve the problem, we need to establish the relationship between the time taken for a radioactive substance to decay to three-fourths of its original quantity (`t_(3/4)`) and the half-life of the substance (`t_(1/2)`).

### Step-by-Step Solution:

1. **Understanding Half-Life**:
The half-life (`t_(1/2)`) is the time required for half of the radioactive substance to decay. Mathematically, this can be expressed using the equation:
\[
t_{1/2} = \frac{0.693}{\lambda}
...