A sample of radioactive material consists of 200 g of nuclide P and 100 g of nuclide Q - AQA - A-Level Physics - Question 27 - 2022 - Paper 2

The half-life of nuclide Q is 4 days, so in 12 days, it will go through 3 half-lives (12 days / 4 days = 3). Using the same formula:

$m = m_0 \left(\frac{1}{2}\right)^n$

where:

• $m_0$ = initial mass = 100 g
• $n$ = number of half-lives = 3

Thus, the remaining mass of nuclide Q is:

$m_Q = 100 \left(\frac{1}{2}\right)^3 = 100 \times \frac{1}{8} = 12.5 \; \text{g}$

Finally, to find the total mass of nuclides P and Q after 12 days, we sum the remaining masses:

$m_{total} = m_P + m_Q = 3.125 \; g + 12.5 \; g = 15.625 \; g$

Rounding this to one decimal place gives us approximately 15.6 g.