True or False Statements :
A fraction `f_(1)` of a radioactive sample decays in one mean life, and a fraction `f_(2)` decays in one half-life, then `f_(1) gt f_(2)`.
Correct Answer - C
Initially whole isotope was X `" "[thereforeX:Y=1:15]`
i.e., `N_(0)=1+15=16` and after decaying into Y
`implies"We have",N=N_(0)e^(-lamdat)implies1=16e^((0.693)/(15xx10^(9))xxt)`
`implies " " 1n ((1)/(16))=e^((1n2)/(t//2))`
`implies "The age of the rck,"t=6.00xx10^(9)yr`...
Correct Answer - C
According to the question, ratio of X:Y is given = 1: 7
`implies(m_(x))/(m_(y))=(1)/(7)implies7m_(x)=m_(y)`
Let the initial total mass is m.
`impliesm_(x)+m_(y)=mimpliesm_(y)/(7)+m_(y)=m`
`implies(8m_(y))/(7)=mimpliesm_(y)=(7)/(8)m`
Only `(1)/(8)` part remains left...
Correct Answer - B
Ratio of X and Y =1 :7
`m_(x)/(m_(y))=(1)/(7)" "m_(y)=7m_(x)` Let the initial total mass =m
`implies m_(x)+m_(y)=m`
`implies(m_(y))/(7)+m_(y)=m`
`(8m_(y))/(7)=mimpliesm_(y)=(7)/(8)m`
Only `((1)/(8))th` part remains undisintegrated, number of half-lives...