An exponential decay law has the general form: A = Ao * e ^ (-kt) =>
A/Ao = e^(-kt)
Half-life time => A/Ao = 1/2, and t = 4.5 min
=> 1/2 = e^(-k*4.5) => ln(2) = 4.5k => k = ln(2) / 4.5 ≈ 0.154
Now replace the value of k, Ao = 28g and t = 7 min to find how many grams of Thalium-207 will remain:
A = Ao e ^ (-kt) = 28 g * e ^( -0.154 * 7) = 9.5 g
Answer 9.5 g.
Answer:
a. The second run will be faster.
d. The second run has twice the surface area.
Explanation:
The rate of a reaction is proportional to the surface area of a catalyst. Given the volume (V) of a sphere, we can find its surface area (A) using the following expression.

The area of the 10.0 cm³-sphere is:

The area of each 1.25 cm³-sphere is:

The total area of the 8 1.25cm³-spheres is 8 × 5.61 cm² = 44.9 cm²
The ratio of 8 1.25cm³-sphere to 10.0 cm³-sphere is 44.9 cm²/22.4 cm² = 2.00
Since the surface area is doubled, the second run will be faster.