A radioactive substance has a half life of 5 days. After 20 days it was foundd the `3 g` of the isotope left in the container. The initial weight of the isotope was
`a `48 g` b. `36 g` c. `18 g` d. `24 g`

Options

A. `a `48 g`
B. b. `36 g`
C. c. `18 g`
D. d. `24 g`

Explanation

To solve the problem step by step, we will use the concept of half-life in radioactive decay.

### Step 1: Understand the concept of half-life
The half-life of a radioactive substance is the time required for half of the substance to decay. In this case, the half-life is given as 5 days.

### Step 2: Calculate the number of half-lives that have passed
Since we need to find the initial weight of the isotope after 20 days, we first determine how many half-lives have passed in that time frame:
- Total time = 20 days
- Half-life = 5 days
- Number of half-lives = Total time / Half-life = 20 days / 5 days = 4 half-lives

### Step 3: Determine the remaining amount after each half-life
If we denote the initial amount of the isotope as \( x \) grams, we can calculate the remaining amount after each half-life:
- After 1 half-life (5 days): \( x/2 \)
- After 2 half-lives (10 days): \( x/4 \)
- After 3 half-lives (15 days): \( x/8 \)
- After 4 half-lives (20 days): \( x/16 \)

### Step 4: Set up the equation based on the remaining amount
According to the problem, after 20 days, the remaining amount of the isotope is 3 grams. Therefore, we can set up the equation:
\[ \frac{x}{16} = 3 \]

### Step 5: Solve for \( x \)
To find the initial weight \( x \), we can rearrange the equation:
\[ x = 3 \times 16 \]
\[ x = 48 \text{ grams} \]

### Conclusion
The initial weight of the isotope was 48 grams. Thus, the correct answer is option (a) 48 g.

---