cesium-137 half-life 30 years

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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