1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Goshia [24]
2 years ago
7

Rutherford once assumed that when the earth was first formed, it contained equal amounts of U-235 and U-238. From this, he was a

ble to determine the age of the earth. Find the Rutherford age of the earth.
Physics
1 answer:
Sindrei [870]2 years ago
3 0

Answer:

  • the Rutherford age of the Earth is 5.942 x 10^9 years

Explanation:

As the radioactive decay is an exponential decay, lets first remember how to solve an exponential decay problem.

In an exponential decay the quantity of substance N at time t is given by:

N(t) = N_0 e^{-\frac{t}{\tau}}

where N_0 is the initial quantity of substance and \tau is the mean lifetime of the substance.

For our problem we start with the same quantity of U-235 and U 238. Lets call this quantity as N_0.

The quantity of U-235 after a time t will be:

^{U-235}N(t) = N_0 e^{-\frac{t}{\tau_{235}}}

and for U-238

^{U-238}N(t) = N_0 e^{-\frac{t}{\tau_{238}}}

Lets call the ratio between this two r. r will be:

r(t) = \frac{^{U-235}N(t)}{^{U-238}N(t)} = \frac{ N_0 e^{ -\frac{t}{ \tau_{235} } } }{ N_0 e^{ -\frac{t}{ \tau_{238} } } }

r(t) = \frac{  e^{ -\frac{t}{ \tau_{235} } } }{ e^{ -\frac{t}{ \tau_{238} } } }

r(t) =  e^{ -\frac{t}{ \tau_{235} }   + \frac{t}{ \tau_{238} }  }

ln ( r(t) ) =   \frac{t}{ \tau_{238} }  - \frac{t}{ \tau_{235} }

ln ( r(t) ) =   t   ( \frac{1}{ \tau_{238} } }  -\frac{1}{ \tau_{235} }  )

\frac{ln ( r(t) )}{ ( \frac{1}{ \tau_{238} }   -\frac{1}{ \tau_{235} }  }  =   t

Now, in the present time the abundance of U-235 is 0.720% and the abundance of U-238 is 99.274%. This gives us a ratio of:

r(t_{present}) =\frac{0.720 \ \%}{99.274 \ \%} = 7.2526 \ 10^{-3}

the mean lifetime of U-235 is

\tau_{235} = 1.016 \ 10^9 years

and the mean lifetime of U-238 is

\tau_{238} = 6.445 \ 10^9 years

so

\frac{1}{ \tau_{238} } }  -\frac{1}{ \tau_{235} } =  \frac{1}{ 6.445 \ 10^9 years } }  -\frac{1}{ 1.016 \ 10^9 years }  = -8.2909 \ 10^{-10} \frac{1}{year}

Taking all this in consideration, we get:

t_{present}=\frac{ln ( r(t_{present}) )}{ ( \frac{1}{ \tau_{238} }  -\frac{1}{ \tau_{235} }  )}

t_{present}=\frac{ln ( 7.2526 \ 10^{-3} )}{-8.2909 \ 10^{-10} \frac{1}{year}}

t_{present}=\frac{ 4.926  }{-8.2909 \ 10^{-10} \frac{1}{year}}

t_{present}= 5.942 \ 10^9 years

You might be interested in
Explain how a book can have energy even if it is not moving.
frutty [35]
Can something have energy even if it's not moving?
All moving objects have kinetic energy. When an object is in motion, it changes its position by moving in a direction: up, down, forward, or backward. ... Potential energy is stored energy. Even when an object is sitting still, it has energy stored inside that can be turned into kinetic energy (motion).


Does a book at rest have energy?
A World Civilization book at rest on the top shelf of a locker possesses mechanical energy due to its vertical position above the ground (gravitational potential energy).



Does a book lying on a table have energy?
The book lying on a desk has potential energy; the book falling off a desk has kinetic energy.
5 0
2 years ago
Do the following calculation and express the final answer in
sammy [17]

Answer:

Explanation:

I got the same thing. So, i don't know but good luck

3 0
1 year ago
Jesse has 200 peanut butter cups and she gives some of them to her friend. How many peanut butter cups did she give her friend?
pychu [463]

Answer:

99 peanut butter

Explanation:

you minus 200 - 101 you get 99 peanut butter

3 0
3 years ago
If the resistance of an electric circuit is 12 ohms and the voltage in the circuit is 60 V, the current flowing through the circ
AnnyKZ [126]
The formula for calculating the current flowing in a circuit is:
I = V /R
Where:
I = current = ?
V = voltage = 60 V
R = resistance = 12 Ohms
I = V /R = 60/ 12 = 5
Therefore, the current flowing through the circuit is 5 A.
7 0
3 years ago
Read 2 more answers
As object has a charge of 4.5 c. did it gain or lose electrons
Tanya [424]
The object lost electrons because one electron adds a negative to the object. <span />
3 0
3 years ago
Other questions:
  • What is the best example of physical contamination?
    6·1 answer
  • A tuna fish body is streamlined to reduce friction. Which describes the type of friction the fish must overcome?
    15·2 answers
  • In fiction, a symbol can be described as __________.
    10·1 answer
  • Question 11 of 11 | Page 11 of 11
    13·1 answer
  • If two children, with masses of 16 kg and 24 kg , sit in seats opposite one another, what is the moment of inertia about the rot
    11·1 answer
  • A guitar string of length L = 0.94 m is oriented along the x-direction and under a tension of T = 92 N. The string is made of st
    5·1 answer
  • How is a light wave likely to react when hitting a shiny opaque object?
    6·1 answer
  • Drag each label to the correct location.
    15·1 answer
  • HELP PLZ 50 POINTS SPACE QUESTION
    6·1 answer
  • When an object is balanced about a pivot, the total clockwise moment must be equal to the total __________ __________. What two
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!