The atomic ratio between the uranium isotopes 238U and 234U in a mineral sample is found to be 1.8× 104 . The half life of 234U is T (1/2)(234)=2.5 × 105 years. The half-life of 238 U is-

Question

The atomic ratio between the uranium isotopes 238U and 234U in a mineral sample is found to be 1.8× 104 . The half life of 234U is T (1/2)(234)=2.5 × 105 years. The half-life of 238 U is- (A) 4.5× 109 years (B) 5.4× 109 years (C) 4.5 years (D) 5.4 years

Tardigrade Admin · Accepted Answer

In radioactive equilibrium λ 1N1=λ 2N2 (N1/T1)=(N2/T2) T2=(N2/N1)× T1 T2=1.8× 104× 2.5× 105 T2=4.5× 109 years

Q. The atomic ratio between the uranium isotopes $^{238} U$ and $^{234} U$ in a mineral sample is found to be $1.8 \times 1 0^{4}$ . The half life of $^{234} U$ is $T_{\frac{1}{2}} (234) = 2.5 \times 1 0^{5}$ years. The half-life of $^{238} U$ is-

$4.5 \times 1 0^{9}$ years

$5.4 \times 1 0^{9}$ years

$4.5$ years

$5.4$ years

In radioactive equilibrium
$λ_{1} N_{1} = λ_{2} N_{2}$
$\frac{N _{1}}{T _{1}} = \frac{N _{2}}{T _{2}}$
$T_{2} = \frac{N _{2}}{N _{1}} \times T_{1}$
$T_{2} = 1.8 \times 1 0^{4} \times 2.5 \times 1 0^{5}$
$T_{2} = 4.5 \times 1 0^{9}$ years

Q. The atomic ratio between the uranium isotopes 238U and 234U in a mineral sample is found to be 1.8×104 . The half life of 234U is T21​​(234)=2.5×105 years. The half-life of 238U is-

4.5×109 years

5.4×109 years

4.5 years

5.4 years