Radon 3.83 days 4.0×10^8 atoms after 12 days

Radon 3.83 days 4.0×10^8 atoms after 12 days

 

 

Radon, 222Rn, is a radioactive gas

that can be trapped in the basement of homes,

and its presence in high concnetrations

is a known health hazard.

 

Radon has a half-life of 3.83 days.

A gas sample contains 4.0×10^8 radon atoms initially.

How many atoms will remain after 12 days have passed

if no more radon leaks in?

 

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방사성 붕괴는 1차 반응.

 

 

 

1차 반응의 반감기

t_1/2 = 0.693 / k

( 참고 https://ywpop.tistory.com/26 )

 

k = 0.693 / t_1/2

= 0.693 / 3.83

= 0.1809 /day

 

 

 

1차 반응 속도식

ln(C_t / C_0) = –k•t

 

ln(C_t / (4.0×10^8)) = –(0.1809) (12)

 

C_t / (4.0×10^8) = e^(–(0.1809) (12))

 

C_t = e^(–(0.1809) (12)) (4.0×10^8)

= 4.6×10^7

 

 

 

답: 4.6×10^7 atoms

 

 

 

 

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