Pu-240 4.60 g 10.0% half-life 5.00 g g/year

Pu-240 4.60 g 10.0% half-life 5.00 g g/year

 

 

4.60 g 플루토늄이 10.0% 붕괴하는데 천년이 걸린다.

1) Pu-240의 반감기는?

2) 2.00 g 플루토늄이 처음 양의 15%로 감소하는데 걸리는 시간은?

3) 5.00 g 플루토늄의 붕괴 속도(g/year)는?

 

 

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?

 

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A.

4.60 g × (10/100) = 0.46 g

 

4.60 – 0.46 = 4.14 g

 

 

1차 반응 속도식

ln(C_t / C_0) = –kt

( 참고 https://ywpop.tistory.com/26 )

 

ln(4.14 g / 4.60 g) = –k(1000 year)

 

k = –ln(4.14 / 4.60) / 1000

= 0.000105 /year

 

 

t_1/2 = 0.693 / k

= 0.693 / 0.000105

= 6600 year

= 6.60×10^3 year

 

 

 

 

B.

2.00 g × (15/100) = 0.3 g

 

 

ln(C_t / C_0) = –kt

 

t = –ln(C_t / C_0) / k

= –ln(0.3 / 2.00) / 0.000105

= 18068 year

= 1.81×10^4 year

 

 

 

 

C.

rate = k[A]

= (0.000105 /year) (5.00 g)

= 0.000525 g/year

= 5.25×10^(-4) g/year

 

 

 

 

[키워드] 플루토늄 반감기 기준문서, Pu-240 반감기 기준문서