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]
3 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]3 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
The centripetal force exerted on stunt motorcyclist Biker Bob while riding on the inner vertical surface of a circular track is:
AlladinOne [14]

Answer:

option C

Explanation:

The correct answer is option C.

The normal force is the force exerted by the biker on the inner vertical surface of the circular track.

When the biker move in the circular track centripetal force is acting on the biker which is being balanced by the normal force.

To overcome the gravitation force on the biker the velocity of the biker should be high such that centripetal acceleration of the biker can overcome the gravity force acting on the biker.

7 0
3 years ago
The gravitational force of a star on an orbiting planet 1 is F1. Planet 2, which is twice as massive as planet 1 and orbits at t
Andrej [43]

Answer:

ratio = 1 : 4.5

Explanation:

If m₁ is the mass of the star and m₂ the mass of the planet, the force of gravity F₁ for planet 1 is given by:

F_1=\frac{Gm_1m_2}{r^2}

The force F₂:

F_2=\frac{Gm_1(2m_2)}{(3r)^2}

The ratio:

\frac{F_2}{F_1}=\frac{2}{9}

8 0
3 years ago
Explain about kinetic theory​
Luden [163]

Answer:

The model, called the kinetic theory of gases, assumes that the molecules are very small relative to the distance between molecules. ... The molecules are in constant random motion, and there is an energy (mass x square of the velocity) associated with that motion. The higher the temperature, the greater the motion.

6 0
3 years ago
How is sound produced? Name its three<br>characteristics.​
nydimaria [60]

Answer:

1.loudness

2.pitch

3.shrillness

5 0
3 years ago
A fisherman is fishing from a bridge and is using a "44.0-N test line." In other words, the line will sustain a maximum force of
vitfil [10]

Answer:

a) 4.485 kg b) 3.94 kg

Explanation:

since the maximum tension the line can stand is 44 N and for question a the speed is constant (acceleration must be zero since the velocity or speed is not changing), F(tension) = mass * acceleration due to gravity (g) .

44 = m * 9.81m/s^2

m = 44/9.81 = 4.485kg

b) F(tension) = ma + mg ( where a is the acceleration of the body and g is the acceleration of the gravity)

44 = m (a +g)

44 = m (1.37 + 9.81)

44/11.18 = m

m = 3.94 kg

3 0
3 years ago
Other questions:
  • What is a shock wave and when is it produced
    12·1 answer
  • How do the units that are used to measure heat differ from the units that are used to measure temperature?
    10·1 answer
  • What is answer of question 7
    11·2 answers
  • I'm very confused on this home work question How did magnetism 'drive' the theory of plate tectonics?
    10·1 answer
  • . A telescope is constructed with two lenses separated by a distance of 25 cm. The focal length of the objective is 20 cm. The f
    9·1 answer
  • If the coefficient of kinetic friction between the puck and the ice is 0.05, how far does the puck slide before coming to rest?
    12·2 answers
  • Please Help!!!!
    10·1 answer
  • How would you use one of Newton’s laws to build a fast car?
    8·2 answers
  • Q1) An action exerted on an object which may change the object's
    8·1 answer
  • What is kinematics??? +_+​
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!