cesium-137 half-life 30 years
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?
a) Find the mass that remains after t years.
m(t) = m(0) × 2^[–t / t_1/2]
> m(0): 최초 질량
> m(t): t 시간 후 남아있는 질량
> t: 시간
> t_1/2: 반감기
m(t) = m(0) × 2^[–t / t_1/2]
= 100 mg × 2^[–t / 30 years]
= 100 × 2^[–t / 30]
답: 100 × 2^[–t / 30] mg
b) How much of the sample remains after 100 years?
m(t) = m(0) × 2^[–t / t_1/2]
m(100) = 100 × 2^[–100 / 30]
= 9.92
답: 9.92 mg
c) After how long will only 1 mg remain?
m(t) = m(0) × 2^[–t / t_1/2]
1 = 100 × 2^[–t / 30]
2^[–t / 30] = 1 / 100 = 0.01
[–t / 30] ln(2) = ln(0.01)
t = –30 × (ln(0.01) / ln(2))
= 199.3
답: 199.3 years
[ 동일 예제 https://ywpop.blogspot.com/2023/12/cesium-137-half-life-30-years_6.html ]
[키워드] 반감기 기준, 반감기 사전, cesium-137 기준, cesium-137 사전
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