after 42 days a 2.0 g sample of phosphorus - 32 contains only 0.25 g of the isotope. what is the half - life…

Explanation:

Step1: Determine the number of half - lives

Use the formula (N = N_0\times\left(\frac{1}{2}\right)^n), where (N = 0.25\space g), (N_0=2.0\space g). Substitute the values into the formula: (0.25 = 2.0\times\left(\frac{1}{2}\right)^n). Then (\frac{0.25}{2.0}=\left(\frac{1}{2}\right)^n), (\frac{1}{8}=\left(\frac{1}{2}\right)^n). Since (\frac{1}{8}=\left(\frac{1}{2}\right)^3), so (n = 3).

Step2: Calculate the half - life

We know that (t=42\space days) and (n = 3). Use the formula (t=n\times t_{1/2}), then (t_{1/2}=\frac{t}{n}). Substitute (t = 42\space days) and (n = 3) into the formula: (t_{1/2}=\frac{42}{3}).

Answer:

(14)