Question

how much of a 400 Gram sample of rubidium-87 would remain after 1 half life

Answer 1

Answer:

200 g.

Explanation:

What is given?

Initial quantity (N₀) = 400 g.

Half-life of rubidium-87 = 4.8 x 10¹⁰ years.

Step-by-step solution:

Let's see the formula to calculate the quantity remaining:

$N(t)=N_0\cdot(\frac{1}{2})^{t\text{ /t}_{\frac{1}{2}}}.{}$

Where N₀ is the initial quantity, t is the time, and t (1/2) is the half-life of the substance, in this case, Rb-87. Based on this, our formula will be:

$N(t)=400\cdot(\frac{1}{2})^{\text{t/\lparen4.8}\cdot10^{10})}$

If we want to find the amount of Rb-87 after 1 half-life, our t would be equal to 4.8 x 10¹⁰ years, so replacing this value in the formula we obtain:

$\begin{gathered} N(4.8\cdot10^{10})=400\cdot(\frac{1}{2})^{4.8\cdot10^{10}\text{/4.8}\cdot10^{10}}, \\ N(4.8\cdot10^{10})=400\cdot(\frac{1}{2})^1, \\ N(4.8\cdot10^{10})=400\cdot(\frac{1}{2}), \\ N(4.8\cdot10^{10})=200\text{ g.} \end{gathered}$

The answer is that after 1 half-life of a 400 g sample of Rb-87, the remaining quantity is 200 g.