Answer to Question #190646 in General Chemistry for Kevin

Question

1) Europium-130 releases 3 alpha particles and 4 beta particles. Write the nuclear equation for this process.

2) How many half-life cycles are required for a sample of radioactive isotope to reach 12.5% of its original mass?

3) Potassium-40 has a half-life of approximately 1.248x109 years. How long does it take for a sample of potassium-40 to decay to 35% of its original mass?

Answer 1

(1) $^{152}_{63}Eu\longrightarrow3\space (^4_2He)+4(_{-1}e)+^{140}_{61}Pm$

(2) 100g to 50g 1 half life

50g to 25 g 1 half life

25 g to 12.5 g 1 half life

3 half life are required

(3)$\dfrac{A(t)}{A_o(t)}=e^{-0.0693\times\dfrac{t}{T_{1/2}}}$

$t=-\dfrac{T_{1/2}}{0.0693}log\bigg(\dfrac{A(t)}{A_o(t)}\bigg)$

$t=6.423\times10^9\space years$