Answer:
40,113 years
Explanation:
To find the age of the sample, you need to use the half-life formula:
[tex]N(t)=N_0(\frac{1}{2})^{t/h[/tex]
In this formula:
------> N(t) = current mass (g)
------> N₀ = initial mass (g)
------> t = time passed (yrs)
------> h = half-life (yrs)
You can plug the given values into the equation and rearrange the formula to find "t".
N(t) = 0.781 g t = ? yrs
N₀ = 100 g h = 5730 yrs
[tex]N(t)=N_0(\frac{1}{2})^{t/h[/tex] <----- Half-life formula
[tex]0.781=100(\frac{1}{2})^{t/5730}[/tex] <----- Insert values
[tex]0.00781=(\frac{1}{2})^{t/5730}[/tex] <----- Divide both sides by 100
[tex]log_{1/2}(0.00781)=log_{1/2}((\frac{1}{2})^ {t/5730})[/tex] <----- Take [tex]log_{1/2}[/tex] of both sides
[tex]7.00 = \frac{t}{5730}[/tex] <----- Solve [tex]log_{1/2}[/tex]
[tex]40,113 = t[/tex] <----- Multiply both sides by 5730
The given sample is 40,113 years .
Half-life, in radioactivity, is the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.
Half-life formula,
[tex]\rm N(t)\;=N_0(\dfrac{1}{2})^\frac{t}{t1/2}[/tex] .......(1)
where,
N(t)=current mass
N₀=initial mass
t=time period
h=half -life
Given,
N(t)=0.781g, t=? yrs, N₀=100g, h=5730 years
[tex]\rm N(t)\;=N_0(\dfrac{1}{2})^\frac{t}{t1/2}[/tex]
put the values, in ......(1)
0.781=100(1/2) [tex]t/5730\\[/tex]
log₁/₂(0.00781)=log₁/₂ ( 1/2)[tex]t/5730[/tex]
7=t/5730
40,113=t
Hence, the given sample is 40,113 years .
Learn more about half-life ,here:
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