÷ has a half-life of 22 years with respect toradioactive decay . The decay follows two parallelpaths : ^227\Ac \to^227\Th and ^227\Ac \to^ 223\Fr. If the percentage of the two daughter nuclides are 2.0 and 98.0, respectively, the decay constant (in year^{–1}) for ^227\Ac \to^227\Th path is closest to

Correct Answer is : 6.3 × 10–4

KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 107 of 120

Marks: +1, -0

÷ has a half-life of 22 years with respect toradioactive decay . The decay follows two parallelpaths :

^227\Ac →^227\Th

and

^227\Ac →^ 223\Fr

. If the percentage of the two daughter nuclides are 2.0 and 98.0, respectively, the decay constant (in year

^{–1}

) for

^227\Ac →^227\Th

path is closest to

Solution:

% Th =

R_1/R_T=2/100

% Ac =

R_1/R_T=98/100

∴

R_1/R_2=2/98

R_T = R_1 + R_2

0.693/22=R_1+98/2R_1

∴

R_1 =6.3 × 10 ^{–4}

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