radon after half a day 6.7×10^(-25) mol

radon after half a day 6.7×10^(-25) mol

 

 

How many radioactive radon atoms are left after half a day

if a gas space initially contained 6.7×10^(-25) mol 222Rn?

(The half life of 222Rn is 3.824 days.)

 

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▶ 참고: Radon has a half-life of 3.83 days

[ https://ywpop.tistory.com/23417 ]

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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 / 3.824

= 0.1812 /day

 

 

 

1차 반응 속도식

ln(C_t / C_0) = –k•t

 

ln(C_t / (6.7×10^(-25) mol)) = –(0.1812 /day) (0.5 day)

 

C_t / (6.7×10^(-25)) = e^(–(0.1812) (0.5))

 

C_t = e^(–(0.1812) (0.5)) (6.7×10^(-25))

= 6.1×10^(-25) mol

 

 

 

(6.1×10^(-25) mol) (6.022×10^23 atoms/mol) = 0.367 atoms

 

 

 

답: 0.37 atoms

 

 

 

 

[참고] 주어진 숫자에 오타가 있는 문제

(6.7×10^(-25) mol) (6.022×10^23 atoms/mol) = 0.403 atoms

 

 

 

 

[키워드] 라돈의 반감기 기준문서