Scientist can determine the age of ancient objects, №14542954, 30.12.2020 16:55

Chemistry

Scientist can determine the age of ancient objects by a method called radiocarbon dating. the bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14c, with a half-life of about 5730 years. vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14c through food chains. when a plant or animal dies, it stops replacing its carbon and the amount of 14c begins to decrease through radioactive decay. therefore, the level of radioactivity must also decay exponentially. a

Step-by-step answer

P Answered by PhD

28,700 years

1. Data:

a) Half-life: 5730 years

b) Final radioactivity: 68%

2. Solution:

a) Determine the number of half-lives undergone

Since, the radioactivity has decreased to 68%, means that the carbon-14 contanined is has been reduced in 32%: 100% - 68% = 32%.32 = 2⁵, meaning that five half-lives have passed since the plant material that formed the parchment fragment died.

b) Compute the time of five half-lives:

5 × half-life time = 5 × 5730 years = 28,650 years.

c) Round to the nearest hundred:

28,650 years ≈ 28,700 years

And that is the age of the parchment.

Chemistry

Scientist can determine the age of ancient objects by a method called radiocarbon dating. the bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14c, with a half-life of about 5730 years. vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14c through food chains. when a plant or animal dies, it stops replacing its carbon and the amount of 14c begins to decrease through radioactive decay. therefore, the level of radioactivity must also decay exponentially. a

Step-by-step answer

P Answered by PhD

28,700 years

1. Data:

a) Half-life: 5730 years

b) Final radioactivity: 68%

2. Solution:

a) Determine the number of half-lives undergone

Since, the radioactivity has decreased to 68%, means that the carbon-14 contanined is has been reduced in 32%: 100% - 68% = 32%.32 = 2⁵, meaning that five half-lives have passed since the plant material that formed the parchment fragment died.

b) Compute the time of five half-lives:

5 × half-life time = 5 × 5730 years = 28,650 years.

c) Round to the nearest hundred:

28,650 years ≈ 28,700 years

And that is the age of the parchment.

Mathematics

Scientist can determine the age of ancient objects by a method called radiocarbon dating. the bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14c, with a half-life of about 5730 years. vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14c through food chains. when a plant or animal dies, it stops replacing its carbon and the amount of 14c begins to decrease through radioactive decay. therefore, the level of radioactivity must also decay exponentially. a

Step-by-step answer

P Answered by PhD

2500 years

Step-by-step explanation:

I'm not quite sure if I'm doing this right myself but I'll give it a shot.

We use this formula to find half-life but we can just plug in the numbers we know to find t.

$A(t)=A_{0}(1/2)^t^/^h$

We know half-life is 5730 years and that the parchment has retained 74% of its Carbon-14. For $A_{0$ let's just assume that there are 100 original atoms of Carbon-14 and for A(t) let's assume there are 74 Carbon-14 atoms AFTER the amount of time has passed. That way, 74% of the C-14 still remains as 74/100 is 74%. Not quite sure how to explain it but I hope you get it. h is the last variable we need to know and it's just the half-life, which has been given to us already, 5730 years, so now we have this.

74=100(1/2)^t^/^5^7^3^0

Now, solve. First, divide by 100.

0.74=(0.5)^t^/^5^7^3^0

Take the log of everything

$log(0.74)=\frac{t}{5730} log(0.5)$

Divide the entire equation by log (0.5) and multiply the entire equation by 5730 to isolate the t and get

$5730\frac{log(0.74)}{log(0.5)} =t$

Use your calculator to solve that giant mess for t and you'll get that t is roughly 2489.128182 years. Round that to the nearest hundred years, and you'll find the hopefully correct answer is 2500 years.

Really hope that all the equations that I wrote came out good and that that's right, this is definitely the longest answer I've ever written.

Mathematics

5.–/1 points scalcet8 3.8.011. ask your teacher my notes question part points submissions used scientist can determine the age of ancient objects by a method called radiocarbon dating. the bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14c, with a half-life of about 5730 years. vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14c through food chains. when a plant or animal dies, it stops replacing its carbon and the amount of 14c begins to decrease through

Step-by-step answer

P Answered by PhD

13,200 years

Explanation:

These steps explain how you estimate the age of the parchment:

1) Carbon - 14 half-life: τ = 5730 years

2) Number of half-lives elapsed: n

3) Age of the parchment = τ×n = 5730×n years = 5730n

4) Exponential decay:

The ratio of the final amount of the radioactive isotope C-14 to the initial amount of the same is one half (1/2) raised to the number of half-lives elapsed (n):

A / Ao = (1/2)ⁿ

5) The parchment fragment had about 74% as much C-14 radioactivity as does plant material on Earth today:

⇒ A / Ao = 74% = 0.74⇒ A / Ao = 0.74 = (1/2)ⁿ ⇒ ln (0.74) = n ln (1/2) [apply natural logarithm to both sides]⇒ n = ln (1/2) / ln (0.74)⇒ n ≈ - 0.693 / ( - 0.301) = 2.30

Hence, 2.30 half-lives have elapsed and the age of the parchment is:

τ×n = 5730n = 5730 (2.30) = 13,179 years Round to the nearest hundred years: 13,200 years

Biology

Scientist can determine the age of ancient objects by a method called radiocarbon dating. the bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14c, with a half-life of about 5730 years. vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14c through food chains. when a plant or animal dies, it stops replacing its carbon and the amount of 14c begins to decrease through radioactive decay. therefore, the level of radioactivity must also decay exponentially. a

Step-by-step answer

P Answered by PhD

1

3688.323 years

Explanation:

Given-

Half life of C = 5730 years

As we know -

$A_{(t)} = A_0e^{kt}$

Where

$A_{(t)} =$ Mass of radioactive carbon after a time period "t"

A_0= initial mass of radioactive carbon

k = radioactive decay constant

t = time

First we will find the value of "k"

$\frac{1}{2} = (1)*e^{k*5730}\\$

On solving, we get -

$e^{5730*k}= 0.5\\5730*k = ln(0.5)\\k = -0.000121$

Now, when mass of 14C becomes % of the plant material on earth today, then its age would be

$A_{(t)} = A_0*e^{(-0.000121*t)}\\A_{(t)}= 0.64*A_0\\0.64*A_0 = A_0*e-^{(0.000121*t)}\\t = 3688.323$ years

Physics

Scientists can determine the age of ancient objects by a method called radiocarbon dating. the bombardment of the upper atmosphere by cosmic rays converts nitrogen to 14c ,a radioactive isotope of carbon, with a half-life of about 5730 years. vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14c through food chains. when a plant or animal dies, it stops replacing its carbon and the amount of 14c begins to decrease through radioactive decay. therefore, the level of radioactivity must also decay exponentially. a

Step-by-step answer

P Answered by PhD

B

Explanation:

A detailed solution to the problem is shown in the image attached. You could study it. The half life, and percentage of C-14 compared to present living sample was given as 13% of that of a living sample.