Question

A certain radioactive substance has a half life of 38 hours. find how long it takes for 90% of the radioactivity to be dissipated

Answer 1

heyy user ur answer...........

x=xoe−ktx=xoe−kt
 

When t = 38 hr, x = 0.5xo
0.5xo=xoe−38k0.5xo=xoe−38k

e−k=0.51/38e−k=0.51/38
 

Hence,
x=xo(0.5t/38)x=xo(0.5t/38)
 

When 90% are dissipated, x = 0.1xo
0.1xo=xo(0.5t/38)0.1xo=xo(0.5t/38)

0.1=0.5t/380.1=0.5t/38

0.138=0.5t0.138=0.5t

t=38ln0.1ln0.5t=38ln⁡0.1ln⁡0.5

t=126.23 hrst=126.23 hrs           

hope this will help u..................@kundan