Answer:
22920 years
Explanation:
half- life : Time in which sample becomes half of its original value.
It is calculated by :
n = t /half-life
Age of the sample = n x (half - life)
here, n = number of half - life
4 ----> 2 ----> 1 ----> 0.5 ---->0.25 (divide the mass each time by 1/2 )
This is equal to 4 - half life
= 4 (5730)
=22920 years
SECOND METHOD
The following equation gives relation between the original Number of species at Zero time (No) and number of species after decays (N) in time t
[tex]N = N_{0}e^{-\lambda t}[/tex]
It is asked to calculate 't'.
[tex]\lambda [/tex] = Decay constant
[tex]\lambda = \frac{0.693}{t_{1/2}}[/tex]
t1/2 = Half life = 5730 years
[tex]\lambda = \frac{0.693}{5730}[/tex]
[tex]\lambda= 1.209\times 10^{-4}[/tex] per year
N= 0.25 g
No = 4.0 g
Insert the parameter in the formula and solve for t
[tex]N = N_{0}e^{-\lambda t}[/tex]
[tex]0.25 = 4e^-{1.209\times 10^{-4}\times t}[/tex]
[tex]\frac{0.25}{4} = e^-{1.209\times 10^{-4}\times t}[/tex]
[tex]0.0625 = e^-{1.209\times 10^{-4}\times t}[/tex]
take ln(natural logarithm) both side,
[tex]ln 0.0625 = ln(e^-{1.209\times 10^{-4}\times t})[/tex]
[tex]-2.75=-1.209\times 10^{-4}\times t}[/tex]
= 22932.9 years (approx to 22920)
