Question

Uranium $237$ has a half-life of about $6.78$ days. If there are $10$ grams of Uranium $237$ now, how much will be left after $2$ weeks?

• A. $4.39$ grams
• B. $3.39$ grams
• C. $2.39$ grams
• D. None of these

Answer 1

The correct option is C $2.39$ grams

We the that the decay algorithm is $-\frac{dx}{dt}=\frac{0.693}{t_{\frac{1}{2}}}x$, where the terms have their usual meanings,

Solving the differential equation gives, $x=x_0{e}^{-\frac{0.693}{t_{\frac{1}{2}}}t}$

Substituting the given values in the obtained equation gives,

$x=10e^{-\frac{0.693}{6.78}14}$

$\therefore x=2.39$ grams will be left