Physics: The half-life for the α decay of uranium is 4.47 × 109 yr. determine the age (in years) of a rock specimen that contains 55.5% of its original number of atoms.

The answer is B.Explanation:PLEASE MARK AS BRAINLIEST...

The half-life for the α decay of uranium is 4.47

davidleew24

12.01.2022

$3.80\times 10^9years$

Explanation:

Half-life of uranium = $4.47\times 10^9$ years

First we have to calculate the rate constant, we use the formula :

$k=\frac{0.693}{4.47\times 10^9\text{years}}$

$k=0.155\times 10^{-9}\text{years}^{-1}$

Now we have to calculate the age of the sample:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant = $0.155\times 10^{-9}\text{years}^{-1}$

t = age of sample = ?

a = let initial amount of the reactant = 100

a - x = amount left after decay process = $\frac{55.5}{100}\times 100=55.5$

Now put all the given values in above equation, we get

$t==\frac{2.303}{0.155\times 10^{-9}}\log\frac{100}{55.5}$

$t=3.80\times 10^9years$

Thus the age of a rock specimen that contains 55.5% of its original number of atoms is $3.80\times 10^9years$

0,0(0 оценок)