An unknown radioactive element decays into non-radioactive substances. In 720 days the radioactivity of a sample decreases by 33 percent. (a) What is the half-life of the element? half-life:_____ (6) How long will it take for a sample of 100 mg to decay to 47 mg? time needed:____

Question

An unknown radioactive element decays into non-radioactive substances. In 720 days the radioactivity of a sample decreases by 33 percent.  (a) What is the half-life of the element? half-life:_____  (6) How long will it take for a sample of 100 mg to decay to 47 mg? time needed:____

Troy Sutton · Accepted Answer

When a radioactive substance decays, it is replaced by a non-radioactive substance.The radioactivity of the sample diminishes by 33% in 720 days.a) To find half life.b) Determine the number of days required for a 100mg sample to degrade to 47mg.Decay constant The decay formula is given by,N(t)=N0e−λtWhere,N(t) = amount of substance left after &#039;t&#039; period.N0&amp;nbsp;= initial amount of substancet = time periodλ&amp;nbsp;= decay constant.When t = 720 is substituted, the amount decreases by 33%.⇒⊂stan⁡ce≤ft=(100−33)%ofN0⇒N(t)=N0e−λ(720)⇒0.67N0=N0e−λ(720)⇒ln⁡(0.67)=−720λ⇒−0.400477567=−720λ⇒λ=0.00055621884a) Half life Now substitute&amp;nbsp;N(t)=N02We have,N(t)=N0e−λt⇒0.5N0=N0e−λt⇒ln⁡(0.5)=−λt⇒−0.693147181=−λtWe know,&amp;nbsp;λ=0.00055621884⇒t=1,246.1771As a result, it takes 1246.1771 days to decay half of the initial substance, or the substance&#039;s half life is 1246.1771 days.b) 100 mg to 47 mg Now substitute N(t) = 47mg and&amp;nbsp;N0=100mgWe have,N(t)=N0e−λt⇒47=(100)e−λt⇒ln⁡(0.47)=−λt⇒−0.755022584=−λtWe know,&amp;nbsp;λ=0.00055621884⇒t=1,357.42001As a result, it takes 1246.1771 days for 100mg to degrade to 47mg.

An unknown radioactive element decays into non-radioactive substances. In 720

Answered question

Answer & Explanation

New Questions in Algebra I