The activity of radionuclide `(""^(100)X)` is 6.023 curie. If the disintegration constatnt is a)`3.7xx10""^(4)sec""^(-1)`,the mass of radionuclide is b)`10""^(-6)`g c)`10""^(-15)`g d)`10""^(-3)`g

Options

A. `10^(-3)` g
B. `10^(-6)` g
C. `10^(-14)` 14 g
D. `10^(-15)` g

Answer

D

Explanation

Rate of decay `=6.023 C`
`=6.023 xx 3.7xx10^(10) dps=2.23 xx 10^(11)` dps
`lambda=3.7xx10^(4) s^(-1)`
Let mass of element = mg
`therefore N_(0)=(mxx6.02xx10^(23))/(226)=m xx 6.02xx10^(21)`
Rate `=lambda N_(0)`
`=2.23 xx 10^(11) = 3.7xx10^(4) xx m xx 6.02xx10^(21)`
`m=(2.23 xx 10^(11))/((3.7xx10^(4))xx(6.02xx10^(21))`
`=10^(5)` g