Half life of a substance is defined as the time period in which a substance becomes just half of it. If it is known that the half life of a substance "DECAY" is 1122 years, then after 4488 years , 80 gm of "DECAY" becomes:

Options

A. a.4 gm
B. b. 20 gm
C. c. 5 gm
D. d. None of these

Answer

To solve the problem, we need to determine how much of the substance "DECAY" remains after 4488 years, given its half-life of 1122 years and an initial amount of 80 grams.

### Step-by-Step Solution:

1. **Understand Half-Life**: The half-life of a substance is the time it takes for half of the substance to decay. For "DECAY," the half-life is given as 1122 years.

2. **Calculate the Number of Half-Lives**:
- We need to find out how many half-lives fit into 4488 years.
- Number of half-lives = Total time / Half-life = 4488 years / 1122 years = 4.

3. **Determine Remaining Quantity**:
- Each half-life reduces the quantity of the substance to half of its previous amount.
- Starting with 80 grams:
- After 1 half-life (1122 years): 80 g / 2 = 40 g
- After 2 half-lives (2244 years): 40 g / 2 = 20 g
- After 3 half-lives (3366 years): 20 g / 2 = 10 g
- After 4 half-lives (4488 years): 10 g / 2 = 5 g

4. **Final Result**: After 4488 years, the remaining amount of "DECAY" is 5 grams.

### Final Answer:
The amount of "DECAY" remaining after 4488 years is **5 grams**.