The half life of radium (226) is 1620 years.
The time takend to convert `10 g` of radium to `1.25 g` is
a. 810 years b. 1620 years
c. 3240 years d. 4860 years

Options

A. a. 810 years
B. b. 1620 years
C. c. 3240 years
D. d. 4860 years

Answer

d. 4860 years

Explanation

`t_(1//2) = 1620` years
`N_(0) = 1.25 g`
We know `K = (2.303)/(t) log (N_(0))/(N)`
`implies (0.693)/(t_(1//2)) = (2.303)/(t) log (10)/(1.25)`
`:.t = (2.303 xx 1620)/(0.693) log (10)/(log (10)/(1.25)) = (0.3)/(log 8) = (0.3)/(3 xx 0.3)`
`:. t_(x%) = t_(1//2) xx 3 = 1620 xx 3 = 4860` years