Technetium 99 is used for brain scans. If a laboratory receives a shipment of 178 g of this isotope, how much will remain after 15 hours? The half life of Technetium 99 is 6 hours.

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Answer 1 · 2017-01-19T11:06:56

The answer is #=31.47g#

We apply the law of dadioactive decay

#m(t)=m_0e^(-lambdat)#

#m(t)=# mass at time t

#m_0=# mass at #t=0#

#lambda=# decay constant

#t_(1/2)=# half life

#lambda=ln2/t_(1/2)=ln2/6=0.1155h^-1#

#t=15h#

#m(15h)=178*e^(-0.1155*15)#

#=178*0.1768=31.47g#

The mass of Technetium 99 remaining after 15 h #=31.47g#