For a substance the average life for α$$-$$ emission is $$1620$$ years and for β$$-emission$$ is $$405$$ years. After how much time the $$1/4$$ of the material remains after α and β emission?

Question

For a substance the average life for α$$-$$ emission is $$1620$$ years and for β$$-emission$$ is $$405$$ years. After how much  time the $$1/4$$ of the material remains after α and β  emission?

Infinity Learn · Accepted Answer

λα$$=11620$$ per year and λβ$$=1405$$ per year and it is given that the fraction of the remained activity $$AA0=14Total$$ decay constant λ$$=$$λα$$+$$λβ$$=11620+1405=1324per$$ year We know that $$A=A0e-$$λt⇒$$t=1$$λ$$logeA0A$$⇒$$t=1$$λ$$loge4=2$$λ$$loge2=324$$ x $$2$$ x $$0.693$$                                           $$=449$$ years.

For a substance the average life for $α$ - emission is 1620 years and for $β$ -emission is 405 years. After how much time the 1/4 of the material remains after $α and β$ emission?

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For a substance the average life for α- emission is 1620 years and for β-emission is 405 years. After how much time the 1/4 of the material remains after α and β emission?

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For a substance the average life for $α$ - emission is 1620 years and for $β$ -emission is 405 years. After how much time the 1/4 of the material remains after $α and β$ emission?