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A radioactive material produces 1160 decays per minute at one time, and 4.0 h later produces 170 decays per minute. whats the half life

Sagot :

Answer:

Half life is 3.23 hours

Explanation:

Given

Decay rate at starting = 1160 decays per minute

Decay rate after 4 hours = 170 decays per minute

As we know know

[tex]N = N_0 *e ^{\Lambda *T}[/tex]

Substituting the given values, we get -

[tex]170 = 1160 *e ^{-4*\Lambda}\\0.1465 = e ^{-4*\Lambda}\\-0.834 = -4 * \Lambda\\\Lambda = 0.834/4\\\Lambda = 0.2085[/tex]

Also

[tex]t_{1/2} = \frac{ln2}{\Lambda}[/tex]

Substituting the given values we get -

[tex]t_{1/2} = =0.693/0.2085\\= 3.23[/tex]hours

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