Question

2. If the half-life of Radon-212 for alpha emission is 38.2 minutes, what initial amount of pure Radon-212 is needed if it is known that 8.2g of it remains after 17.0 minutes of an experiment?

Answer 1

Answer 2

Given:

• Half-life (t₁/₂) of Radon-212 = 38.2 minutes

• Remaining amount (N) after 17.0 minutes = 8.2 g

• Initial amount (N₀) = ?

• 
  

Formula:

$$N=N_0\times {\left(\frac{1}{2}\right)}^{\frac{t}{t_{1\mathrm{/}2}}}$$

1. Exponent Calculation:

   $$\frac{t}{t_{1\mathrm{/}2}}=\frac{17.0}{38.2}\approx 0.445$$

2. Decay Factor Calculation:

   $${\left(\frac{1}{2}\right)}^{0.445}\approx e^{-0.445\ln (2)}$$$$\approx e^{-0.445\times 0.693}$$$$\approx e^{-0.308}$$$$\approx 0.735$$

3. Solve for $N_0$ (initial amount):

   $$8.2=N_0\times 0.735$$$$N_0=\frac{8.2}{0.735}\approx 11.16\text{ g}$$

Verification:

If we start with ~11.16 g, after 17.0 minutes:

$$11.16\times 0.735\approx 8.2\text{ g}$$