If the half life of a radioactive substance is 4 days. Calculate the time required to decrease the concentration of 1/8th of original??

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Answer 1 · 2018-04-06T14:24:00

Half life of a radioactive substance is defined as the time taken for it to degrade to 1/2 of its original quantity.

I like looking at the problem this way

#1->1/2->1/4->1/8#

So it reaches #1/8#th of the original after #3#(counting the number of arrows) half lives.

The time required, therefore, to decrease the concentration of 1/8th of original would be

#=3xx4 " days"#

# = 12 " days"#

#color(white)(ddddwwwwwwwwwdd#

Now, this is the formula approach.

Let #N_0# be the original quantity and #N# be the new quantity then,

#N / (N_0)= 1/2^(t/T)#

#N / (N_0)= 1/8# #color(white)(ddddwwwwwwwwwdd# #["given that " N = N_0/8]#

#=>1/8 = 1/2^(t/T)#

#=> 2^(t/T)=8=2^3#

#=>t/T = 3#

#=> t= 3xx4 " days"= 12 " days"# #color(white)(ddd# #["given that " T=4 " days"#]