A chemist prepares `1.00 g` of pure `._(6)C^(11)`. This isotopes has half life of 21 min, decaying by the equation:
a. What is the rate of disintegration per second (dps) at starts ?
b. What is the activity and specific activity of `._(6)C^(11)` at start?
c. How much of this isotope `(._(6)C^(11))` is left after 24 hr its preparation?

Explanation

Applying `- (dN)/(dt) = lambda N_(0)`
`= (0.693)/(21 xx 60) xx (1 xx 6.02 xx 10^(23))/(11)`
`= 3 xx 10^(19) dps`
b. Acitivity `= (3 xx 10^(19))/(3.7 xx 10^(10))` (1 curie `= 3.7 xx 10^(10) dps)`
`= 8.108 xx 10^(8)` curie
Specifics activity `= 3 xx 10^(19) xx 10^(3) xx 10^(22)` dis `(kg s)^(-1)`
`= 8.108 xx 10^(11)` curie
c. Applying `N = N_(0) ((1)/(2))^(n) [n = (t)/(t_(1//2)) = (24 xx 60)/(21) = 68.57]`
`N = 1 xx ((1)/(2))^(68.57) = 2.29 xx 10^(-21) g`