Answer:
The correct answer is option C.
Explanation:
Half life of the uranium-238=\(t_{\frac{1}{2}}=4.5 \text{billion years}\)
Decay constant =\(\lambda\)
\(\lambda =\frac{0.693}{t_{\frac{1}{2}}}\)
\(\lambda =\frac{0.693}{4.5 \text{billion years}}=0.154 ({\text{billion year})^{-1}\)
Let the initial amount of U-238 be x
And the present amount of U-238 be x'.
\(A=A_o\times e^{-\lambda t}\)
\(A_o\) = Initial amount
A = Amount left after time t
\(x'=x\times e^{-0.154 ({\text{billion year})^{-1}\times 4.5\text{billion years}}\)
\(x'=x\times 0.500\)
Percentage of left amount:
\(\%=\frac{A}{A_o}\times 100\)
\(\%=\frac{x\times 0.5000}{x}\times 100=50.00\%\)
Hence,the correct answer is option C.
