Respuesta :
w=m₁/m₀=2^(-t/T)
t=4.6·10⁹ years
T=5·10¹⁰ years
w=2^(-4.6·10⁹/5·10¹⁰)
w=0.9382
w=93.82%
t=4.6·10⁹ years
T=5·10¹⁰ years
w=2^(-4.6·10⁹/5·10¹⁰)
w=0.9382
w=93.82%
Answer:
the ratio of parent to daughter = 15.38 : 1
Explanation:
The radioactive disintegration is considered to be first order reaction.
The relation between first order rate constant and the half life is:
[tex]k=\frac{0.693}{t_{\frac{1}{2} }}[/tex]
Let us calculate the rate constant from half life as
[tex]k=\frac{0.693}{50}=0.01386 (billionyr)^{-1}[/tex]
The rate law expression for first order reaction is
[tex]kt=ln\frac{[A0]}{At}[/tex]
Where
A0 = initial amount of rubidium isotope = say 100
At= final amount of rubidium isotope after 4.6 billion years
putting all values
[tex]0.1386X4.6=ln\frac{100}{At}[/tex]
1.065=100/At
At=93.897
The amount of daughter isotope formed =100-93.897 = 6.103
the ratio of parent to daughter = 93.897:6.103 = 15.38 : 1
