Question

The half-life of \( _{43}\text{Tc}^{99} \) is 6 hours. If 12 mg of \( _{43}\text{Tc}^{99} \) is injected to a patient, after 24 hours how much Tc will be left in the patient’s body? (A) 0 mg

• A. 0.75 mg
• B. 3 mg
• C. 6 mg
• D. 12 mg
• E.

Hint:

Every half-life halves the quantity.

Answer 1

The Correct Option is B

Concept: Radioactive decay law
Amount remaining after $n$ half-lives: \[ N = N_0 \left(\frac{1}{2}\right)^n \]

Step 1: Determine number of half-lives
Given $n = 4$

Step 2: Substitute values
\[ N = 12 \times \left(\frac{1}{2}\right)^4 \] \[ N = 12 \times \frac{1}{16} \]

Step 3: Calculate
\[ N = 0.75 \text{ mg} \] Final Answer:
\[ \boxed{0.75 \text{ mg}} \] Note:
With each half-life, the quantity reduces to half, leading to exponential decay.