Let the age of the planet be = t years
Given,
U238o:U235o=1:1
U238t:U235t=64:1
Now, λ238.t=lnU2380U238t and λ235.t=lnU2350U235t
Hence,(λ238−λ235)t=ln(U2380U238t×U235tU2350)
⇒ln 2×(14.45×109−17×108)=ln(164)
⇒ln 2×(4.45−0.74.45×0.7×109)t=ln(641)⇒ln 2×(3.754.45×0.7×109)t=6 ln 2
⇒t=4.45×0.7×109×63.75=4984×106 years.