How did you get this? k===0.693t1/20.69315 hrs0.0462 hrs−1k=0.693t1/2=0.69315 hrs=0.0462 hrs 0.693 a 102.0 nanogram(ng) sample of sodium-24 was stored in a lead-lined cabinet for 2.5 days How much sodium-24 remained? The half-life os sodium -24 is 15 hours _________ ng sodium -24 remain check_circle Expert Answer thumb_up thumb_down Step 1 Radioactive decay is a first order reaction. Conversion of days into hours: 1 day2.5 days===24 hrs2.5×2460 hrs1 day=24 hrs2.5 days=2.5×24=60 hrs Calculation of k: k===0.693t1/20.69315 hrs0.0462 hrs−1k=0.693t1/2=0.69315 hrs=0.0462 hrs-1 Step 2 Radioactive decay is a first order reaction, therefore: [A]=[Ao] e−kt[A]=[Ao] e-kt where [A] is the final amount remained at time t, [Ao] is the initial amount. Putting values: [A]====102.0 ng×e−0.0462 hrs−1×60 hrs102.0 ng×e−2.772102.0 ng×0.062546.38 ng[A]=102.0 ng×e-0.0462 hrs-1×60 hrs=102.0 ng×e-2.772=102.0 ng×0.06254=6.38 ng Thus 6.38 ng of sodium-24 remained.
How did you get this?
k===0.693t1/20.69315 hrs0.0462 hrs−1k=0.693t1/2=0.69315 hrs=0.0462 hrs
0.693
a 102.0 nanogram(ng) sample of sodium-24 was stored in a lead-lined cabinet for 2.5 days How much sodium-24 remained? The half-life os sodium -24 is 15 hours
_________ ng sodium -24 remain
Expert Answer
Radioactive decay is a first order reaction.
Conversion of days into hours:
1 day2.5 days===24 hrs2.5×2460 hrs1 day=24 hrs2.5 days=2.5×24=60 hrs
Calculation of k:
k===0.693t1/20.69315 hrs0.0462 hrs−1k=0.693t1/2=0.69315 hrs=0.0462 hrs-1
Radioactive decay is a first order reaction, therefore:
[A]=[Ao] e−kt[A]=[Ao] e-kt
where [A] is the final amount remained at time t, [Ao] is the initial amount.
Putting values:
[A]====102.0 ng×e−0.0462 hrs−1×60 hrs102.0 ng×e−2.772102.0 ng×0.062546.38 ng[A]=102.0 ng×e-0.0462 hrs-1×60 hrs=102.0 ng×e-2.772=102.0 ng×0.06254=6.38 ng
Thus 6.38 ng of sodium-24 remained.
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