The half-life of the isotope `._(11)Na^(24)`, is 15h. How much time does it take for `(7)/(8)`th of a same of this isotope to decay?

Options

A. 75 h
B. 65 h
C. 55 h
D. 45 h

Answer

C

Explanation

If N is the number of disintegrated nucleus in time t,
then `N=N_(0)(1-e^(-lamdat))`
`implies (N_(0)-N)/(N_(0))=e^(-lamdat)`
`therefore (1)/(8)=e^(-lamdat) implies 8e^(lamdat)`
`implies3ln2=lamdat`
`implies lamda=(3xx0.693)/(15)`
Half-life period, `t_(1//2)=(0.693)/(3xx0.693)xx15=5` min