The half life of radium is about 1200 years.if hundred gram of radium is existing now than 25g will remain undecayed after

Options

A. 1800 years
B. 2400 years
C. 2800 years
D. 3200 years

Answer

To solve the problem, we need to determine how much time it takes for 100 grams of radium to decay to 25 grams, given that the half-life of radium is 1200 years.

### Step-by-Step Solution:

1. **Understanding 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 of radium is given as 1200 years.

2. **Initial Amount**:
We start with an initial amount of radium, which is 100 grams.

3. **First Half-Life**:
After the first half-life (1200 years), half of the initial amount will remain:
\[ \text{Remaining amount} = \frac{100 \text{ grams}}{2} = 50 \text{ grams} \]
So, after 1200 years, we have 50 grams of radium left.

4. **Second Half-Life**:
After the second half-life (another 1200 years), half of the remaining amount will decay:
\[ \text{Remaining amount} = \frac{50 \text{ grams}}{2} = 25 \text{ grams} \]
Thus, after another 1200 years (totaling 2400 years), we have 25 grams of radium left.

5. **Total Time Calculation**:
To find the total time taken for the amount to decay from 100 grams to 25 grams, we add the time taken for each half-life:
\[ \text{Total time} = 1200 \text{ years} + 1200 \text{ years} = 2400 \text{ years} \]

### Final Answer:
The total time taken for 100 grams of radium to decay to 25 grams is **2400 years**.

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