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