Question

The half life period of a radioactive element is 140 days. After 560 days 1 g of element reduced to:

• A. ( (1)/(8) ) g
• B. ( (1)/(2) ) g
• C. ( (1)/(16) ) g
• D. ( (1)/(4) ) g

Hint:

You can also solve this by simple division: Start: 1 g 1ˢᵗ 0.5 g 2ⁿᵈ 0.25 g 3ʳᵈ 0.125 g 4ᵗh 0.0625 g (which is 1/16 g).

Answer 1

The Correct Option is C

Concept: The amount of a radioactive substance remaining after a certain time can be determined by the number of half-lives that have passed. The general formula for the amount remaining (N) is: N = N₀ ( (1)/(2) )ⁿ Where: • N₀ is the initial mass. • n is the number of half-lives, calculated as n = Total Time (T)Half-life (t₁/₂).
Given: • Half-life (t₁/₂) = 140 days • Total time (T) = 560 days n = (560)/(140) = 4 So, the element undergoes 4 half-lives.
Initial mass (N₀) = 1 g. Using the formula: N = 1 g × ( (1)/(2) )⁴ N = 1 × (1)/(16) = (1)/(16) g