Two isotopes p and q of atomic weight 10 and 20, respectively are mixed in equal amount by weight. After 20 days their weight ratio is found to be 1 : 4. Isotope p has a half-life of 10 days. The half-life of isotope q is:
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The half life of isotope q will be 5 days.
Initial mole of p = w / 10
q = w / 20
Final mole of p = w1 / 5 x 10
q = w2 / 5 x 20
As,
isotope = No / N isoptope = e ^ λisotope x 20
p w x 5 x 10 / 10 x w1 = e ^ λp x 20 ------ 1
q w x 5 x 20 / 20 x w1 x 4 = e ^ λq x 20 ------2
4 = e ^ ( λp - λq ) x 20
20 [ 0.693 / t1/2 - 0.693 / 10 ] = loge 4
t 1 / 2 = 5
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