Question

Bismuth has a half-life period of $5$ days. A sample originally has a mass of $1000\text{ mg}$, then the mass of Bismuth after $30$ days is

• A. $16.625\text{ mg}$
• B. $13.625\text{ mg}$
• C. $14.625\text{ mg}$
• D. $15.625\text{ mg}$

Hint:

When calculations involve simple integers, you can quickly write out the stepwise division by 2: $$1000 \rightarrow 500 \rightarrow 250 \rightarrow 125 \rightarrow 62.5 \rightarrow 31.25 \rightarrow 15.625$$ Counting exactly 6 steps yields the solution effortlessly without managing large exponents.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Determine the remaining mass of Bismuth after 30 days, given initial mass of 1000 mg and half-life of 5 days.

Step 2: Key Formula or Approach:
Use the radioactive decay formula: N = N₀(1/2)ⁿ, where n = Total time / Half-life period.

Step 3: Detailed Explanation:
Given N₀ = 1000 mg, T₁/₂ = 5 days, t = 30 days. Number of half-lives: n = 30/5 = 6. Remaining mass: N = 1000 × (1/2)⁶ = 1000/64 = 15.625 mg.

Step 4: Final Answer:
The remaining mass is 15.625 mg, option (D).