Question

Plutonium-240 (Pu-240) is a byproduct of the nuclear reaction that takes place in a reactor. It takes one thousand years for 10.0% of a 4.60-g sample to decay.
A. What is the half-life of PU-240?
B. How long will it take to reduce a 2.00-g sample to 15% of its original amount?
C. What is the rate of decay of a 5.00-g sample in g/year?

Answer 1

Answer on Question #49600, Chemistry, Other

**Task:**

Plutonium-240 (Pu-240) is a byproduct of the nuclear reaction that takes place in a reactor. It takes one thousand years for 10.0% of a 4.60-g sample to decay.

A. What is the half-life of PU-240?

B. How long will it take to reduce a 2.00-g sample to 15% of its original amount?

C. What is the rate of decay of a 5.00-g sample in g/year?

**Answer:**

A. Half-life of an element is a period, during which a half amount of the element is decayed.

$$[Pu - 240] = 4,6 - 0,1 \cdot 4,6 = 4,14\ g$$ $$\ln 4,6 - \ln 4,14 = k(1000\ y)\quad k = 1.05 \cdot 10^{-4}\ y^{-1}$$ $$t_{1/2} = \frac{0,693}{1.05 \cdot 10^{-4}\ y^{-1}} = 6,6 \cdot 10^{-3}\ y$$

B.

$$[Pu - 240] = 0,15 \cdot 2.00 = 0,30\ g$$ $$\ln 2,00 - \ln 0,30 = (1,05 \cdot 10^{-4}\ y^{-1})\ t\quad t = 1.8 \cdot 10^{4}\ y^{1}$$

C. Rate = $(1.05 \cdot 10^{-4}\ y^{-1}) \cdot 5,00 = 5.25 \cdot 10^{-4}\ g / y$

http://www.AssignmentExpert.com/