Question

The half-life of radium is about 1600 years. Of 100g of radium existing now, 25g will remain undecayed after

• A. 6400 years
• B. 2400 years
• C. 3200 years
• D. 4800 years

Answer 1

The Correct Option is C

To solve this problem, we need to understand the concept of radioactive decay and how to calculate the time elapsed based on the half-life of a substance.

Radium has a half-life of 1600 years. The half-life is the time taken for half of the radioactive atoms in a sample to decay. So, every 1600 years, the amount of radium will reduce to half its previous amount.

Let's calculate the time required for 100g of radium to decay to 25g using the concept of half-life:

1. Initially, we have 100 grams of radium.
2. After 1600 years, half of 100g will remain: 100 \div 2 = 50 \text{ grams} .
3. After another 1600 years (total 3200 years), half of 50g will remain: 50 \div 2 = 25 \text{ grams} .

Therefore, after 3200 years, 25 grams of the original 100 grams of radium will remain undecayed.

Thus, the correct answer is: 3200 years.