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?

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a) Find the mass that remains after t years.

> 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

[키워드] 반감기 기준, 반감기 사전, cesium-137 기준, cesium-137 사전