The decay constant for a radio nuclide, has a value of `1.386 day^(-1)`. After how much time will a given sample of this nuclide get reduced to only 6.25% of its present number ?

Explanation

To solve the problem, we need to determine the time it takes for a radioactive nuclide to decay to 6.25% of its original amount, given a decay constant (λ) of 1.386 day^(-1).

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Decay constant (λ) = 1.386 day^(-1)
- We need to find the time (t) when the sample is reduced to 6.25% of its original amount.

2. **Convert Percentage to Fraction:**
- 6.25% can be expressed as a fraction:
\[ \frac{N}{N_0} = \frac{6.25}{100} = \frac{1}{16} \]

3. **Relate Fraction to Half-Lives:**
- The relationship between the remaining quantity and the number of half-lives (N) is given by:
\[ \frac{N}{N_0} = \left(\frac{1}{2}\right)^N \]
- Setting this equal to our fraction:
\[ \left(\frac{1}{2}\right)^N = \frac{1}{16} \]
- Recognizing that \( \frac{1}{16} = \left(\frac{1}{2}\right)^4 \), we find:
\[ N = 4 \]

4. **Calculate the Half-Life (t_1/2):**
- The half-life (t_1/2) can be calculated using the formula:
\[ t_{1/2} = \frac{0.693}{\lambda} \]
- Substituting the value of λ:
\[ t_{1/2} = \frac{0.693}{1.386} = 0.5 \text{ days} \]

5. **Calculate Total Time (t):**
- The total time (t) for the sample to decay to 6.25% is given by:
\[ t = N \times t_{1/2} \]
- Substituting the values:
\[ t = 4 \times 0.5 \text{ days} = 2 \text{ days} \]

### Final Answer:
The time required for the sample to reduce to 6.25% of its original amount is **2 days**.