Answer:
λ(Decay constant) = 0.0492sec-¹
The relationship between Decay Constant and Half life (t½)
λ=0.693/t½
given the decay constant as 0.0492
We can get the Half life
t½ = 0.693/0.0492
t½= 14.09secs.
N = N°(½)ⁿ
Where N= Remaining Amount of the original Compound
N° = Original Amount of compound.
n is simply a tern used to represent the ratio of time taken/half life
In other words
n=t/t½
Given N°=0.656 mol/L
N=0.433mol/L
0.433 = 0.656(½)ⁿ
(½)ⁿ = 0.433/0.656
(½)ⁿ = 0.660
Taking the Natural Log(Ln) of both sides
Ln(½)ⁿ = Ln(0.66)
nLn(½) = -0.4155
n(-0.6931) = -0.4155
n= 0.4155/0.6931
n= 0.5995.
n = time/half life
t = half life x n
t = 14.09 x 0.5995
t = 8.45secs.