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 long it will take 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 substance is the time it takes for half of the substance to decay. For radium, this half-life is 1200 years.

2. **Initial Amount**: We start with 100 grams of radium.

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

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

5. **Total Time Calculation**: To find out how long it takes for the initial 100 grams to decay to 25 grams, we sum the two half-lives:
\[ \text{Total time} = 1200 \text{ years} + 1200 \text{ years} = 2400 \text{ years} \]

### Final Answer:
After 2400 years, 25 grams of radium will remain undecayed.

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