cesium-137 half-life 30 years. 속도상수로 계산
The half-life of cesium-137 is 30 years.
Suppose we have a 100 mg sample.
a) Find the mass that remains after t years.
b) How much of the sample remains after 100 years?
c) After how long will only 1 mg remain?
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a) Find the mass that remains after t years.
[반감기의 정의로부터, 속도 상수(k) 계산]
> P_0 = 100 mg
> t = 30 years
---> 30 years 후 질량 = 50 mg = P_t
equation for decay
P_t = P_0 e^(kt)
( 참고 https://ywpop.tistory.com/26 )
( 참고: e^(kt) 대신 e^(–kt)를 사용해도 된다. )
50 = 100 × e^(30k)
e^(30k) = 50 / 100 = 0.5
30k × ln(e) = ln(0.5)
( 참고: ln(e) = 1 )
k = ln(0.5) / 30
= –0.023105
P_t = 100 × e^(–0.023105 × t)
답: 100 × e^(–0.023105 × t) mg
b) How much of the sample remains after 100 years?
P_t = 100 × e^(–0.023105 × t)
P_100 = 100 × e^(–0.023105 × 100)
= 9.92
답: 9.92 mg
c) After how long will only 1 mg remain?
P_t = 100 × e^(–0.023105 × t)
1 = 100 × e^(–0.023105 × t)
e^(–0.023105 × t) = 1 / 100 = 0.01
(–0.023105 × t) ln(e) = ln(0.01)
t = –ln(0.01) / 0.023105
= 199.3
답: 199.3 years
[ 동일 예제 https://ywpop.blogspot.com/2023/12/cesium-137-half-life-30-years.html ]
[키워드] 반감기 기준, 반감기 사전, cesium-137 기준, cesium-137 사전
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