What is the decay constant of 23892u whose half-life is 4.5×109year?

Answer is: decay constant for uranium-238 is 1,54·10⁻¹⁰ 1/y.
The half-life for the radioactive decay of U-238 is 4.5 billion years and is independent of initial concentration.
t1/2 = 4.5·10⁹ y.
λ = 0,693 ÷ t1/2.
λ= 0,693 ÷ 4.5·10⁹ y.
λ = 1,54·10⁻¹⁰ 1/y.
λ - decay constant.
Decay constant is proportionality between the size of a number of radioactive atoms (in this example uranium) and the rate at which the number of radioactive uranium atoms decreases because of radioactive decay. 

Spontaneity tell us the direction of the reaction, but not how fast it goes. gibbs free energy brings together enthalpy, entropy and temperature in one easy formula. g = h - ts. and, finally the sign of delta g is always negative for a spontaneous reaction.