Uranium-235 decays to thorium-231 with a half-life of 700 million years. When a rock was formed, it contained 6400 million uranium-235 nuclei and no thorium-231 nuclei. Show that after 2100 million years there are seven times more thorium nuclei than uranium nuclei in the rock.

Answers

Answer 1

Answer:

proof in explanation

Explanation:

First, we will calculate the number of half-lives:

[tex]n = \frac{t}{t_{1/2}}[/tex]

where,

n = no. of half-lives = ?

t = total time passed = 2100 million years

[tex]t_{1/2}[/tex] = half-life = 700 million years

Therefore,

[tex]n = \frac{2100\ million\ years}{700\ million\ years}\\\\n = 3[/tex]

Now, we will calculate the number of uranium nuclei left ([tex]n_u[/tex]):

[tex]n_u = \frac{1}{2^{n} }(total\ nuclei)\\\\n_u = \frac{1}{2^{3} }(6400\ million)\\\\n_u = \frac{1}{8}(6400\ million)\\\\n_u = 800\ million[/tex]

and the rest of the uranium nuclei will become thorium nuclei ([tex]u_{th}[/tex])

[tex]n_{th} = total\ nuclei - n_u\\n_{th} = 6400\ million-800\ million\\n_{th} = 5600\ million[/tex]

dividing both:

[tex]\frac{n_{th}}{n_u}=\frac{5600\ million}{800\ million} \\\\n_{th} = 7n_u[/tex]

Hence, it is proven that after 2100 million years there are seven times more thorium nuclei than uranium nuclei in the rock.


Related Questions

What is the electric field strenght in units of N/C if the flux through a 2.0m by 1.0m rectangular surface is 396Nm2/C, if the electric field is uniform, and if the plane of the surface is at an angle of π/3 radians with respect to the direction of the field ?

Answers

Answer:

The appropriate answer is "396 N/C".

Explanation:

The give values are:

Rectangular surface,

[tex]\Phi_e=396 \ N.m^2/C[/tex]

[tex]a = 2 \ m[/tex]

[tex]b = 1 \ m[/tex]

Angle,

[tex]\theta =\frac{\pi}{3} \ radian[/tex]

Now,

The area of rectangle (A) will be:

=  [tex]a\times b[/tex]

=  [tex]2\times 1[/tex]

=  [tex]2 \ m^2[/tex]

hence,

The electric field strength will be:

⇒  [tex]\Phi_e=E.A Cos \theta[/tex]

or,

⇒  [tex]E=\frac{\Phi_e}{ACos \theta}[/tex]

On putting the given values, we get

⇒      [tex]=\frac{396}{2\times Cos(\frac{\pi}{3} )}[/tex]

⇒      [tex]=\frac{396}{2\times 0.5}[/tex]

⇒      [tex]=\frac{396}{1}[/tex]

⇒      [tex]=396 \ N/C[/tex]

How does the circuit structure affect the brightness of a bulb? How does the circuit structure affect the energy required to keep bulbs lit? Summarize some of the tradeoffs (pros and cons) of wiring bulbs in series vs. Parallel.

Answers

Answer:

Part A

The relationship between the circuit structure and the brightness of the bulb are;

The brightness of the bulb depends on the voltage to which the bulb is connected to

Bulbs connected in parallel, are connected directly to the voltage of the power source and are therefore brighter than bulbs arranged in series due to the reduced potential difference between bulbs in series and the voltage source

Part B

Given that bulbs are brighter when arranged in parallel, they require more energy to keep the bulbs lit than when they are arranged in series

Part C

The pros and cons of wiring bulbs in series and parallel are;

Series Circuits Disadvantage

i) A failure of one bulb arranged in series can lead to a failure of the circuit

ii) Bulbs arranged in series are not as bright as bulbs arranged in parallel

iii) When the number of bulbs arranged in a series are increased, the brightness decreases

iv) The bulbs cannot be controlled independently

Advantages of Series Circuits

i) Series circuits consume less energy and the batteries last longer when the attached bulbs are arranged in series

Disadvantage of bulbs arranged in parallel

i) The battery power quickly consumed

The Advantages of Bulbs in Parallel

i) The bulbs light brighter when they are in parallel

ii) The bulbs can be individually controlled

iii) The current can flow through more than one path way

iv) When one bulb fuses, the others in the circuit keep working

Explanation:

Below is a single of DNA, What is the complementary base pair for RNA?
AGC, CGT, ATA, GAT

Answers

It’s GAT because I just learned about this

What causes mechanical wave motion

Answers

Answer:

A disturbance or vibration in matter

Explanation:

Answer:

A mechanical wave is a distance in matter that transfer energy through the matter. A mechanical wave starts when matter is disturbed. A source of energy is needed to disturb matter and start a mechanical wave.

A 20×10⁹charge is moved between two points A andB that are 30mm apart and have an electric potential difference of 600v between them. calculate a) the electric field strength between A and B b)the work done on the charge.​

Answers

Answer:

John Felix Anthony Cena is an American professional wrestler, actor, and television presenter. He is currently signed to WWE. Born and raised in West Newbury, Massachusetts, Cena moved to California in 1998 to pursue a career as a bodybuilder.

Explanation:

A device used to measure small currents is a(n)
a.
electric motor.
b.
commutator.
c.
armature.
d.
galvanometer.

Answers

Answer:

d.

galvanometer.

Explanation:

Galvanometer is the device which is used for measuring small currents due to changing magnetic field.

It is D galvanometer ok

A student is holding a marble in his hand. What are the equal and opposite forces that are acting on it?

Answers

Answer:

Gravity and his hand

Explanation:

According to the special theory of relativity, what is the fourth dimension?

Answers

Explanation:

A four-dimensional space is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.

According to the special theory of relativity, the fourth dimension is time. The special theory of relativity, proposed by Albert Einstein in 1905, revolutionized our understanding of space and time.

It states that space and time are interconnected and form a four-dimensional framework known as spacetime. In this framework, three dimensions correspond to space (length, width, and height), and the fourth dimension is time. Einstein's theory introduced the concept of time dilation, which means that time can appear to pass differently for observers in relative motion. This idea challenges the notion of time as an absolute quantity and demonstrates that it is influenced by an observer's relative motion and gravitational fields.

To visualize the fourth dimension, consider a space-time diagram where an object's position in space is plotted against time. Each point on the diagram represents an event, combining its spatial coordinates with the time at which it occurred. This four-dimensional representation allows us to understand the relationship between space and time in a unified framework.

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who is the richest artist in the Gambia 2020​

Answers

Answer:

Jaliba Kuyateh is the most famous and wealthiest Gambian musician.

Which type of uninterruptible power supply uses AC power to continuously charge its battery, while also providing power to devices through the battery?

Answers

Answer:

An online UPS.

Explanation:

An online UPS is a type of uninterruptible power supply uses AC power to continuously charge its battery, while also providing power to devices through the battery. It combines the inverter and rectifier to provide power to the alternating current (AC) load while supplying alternating current (AC) power during an outage to the load through the inverter.

Basically, an uninterruptible power supply unit is used to provide constant power supply to an electrical device, especially during a power outage.

A 100kg linebacker runs with a velocity of 5m/s towards an 88kg quarterback, who begins to back up
with a velocity of 2m/s to avoid being sacked

a.What is the momentum of the linebacker-quarterback system?

b.the quarterback is unsuccessful in evading the linebacker and gets sacked. what is the velocity of the football players just after the linebacker dives in for a tackle if the 2 players move as one clump?

Answers

Report this clown who put the first answer he’s trying to get your ip

A 7 cm thick and 20 cm long wedge is used to pierce a 3cm long log of diameter 20cm what is the velocity ratio of the wedge

Answers

Answer:

The velocity ratio of the wedge is 0.15

Explanation:

Use the following formula to calculate the velocity ratio

Velocity Ratio = Distance Moved by effort / Distance moved by Load

Where

Distance Moved by effort = 3cm

Distance moved by Load = 20 cm

Placing values in the formula

Velocity Ratio = 3cm / 20 cm

Velocity Ratio = 0.15

The water hyacinth lives in lakes and ponds it forms large floating mats of plants because it does not root in soil which adaptation lets it get nutrients directly from the water is it A.1 curly leaves B.Trailing C.Sturdy stems D. Upright flowers

Answers

Answer:

C. Sturdy stems

Explanation:

Sturdy stems is the adaptation that enables water hyacinth to get nutrients directly from the water because there is no roots are present for the absorption of nutrients from water. The hollow bulbous stem below each leaf of water hyacinth allows the plant to get nutrients from the water. This hollow bulbous stem allow the plants to float on the water surface, keeping the leaves and flowers above the water so they don't rot.

Every second, the Sun converts about 600 million tons of hydrogen into 596 million tons of helium. The remaining 4 million tons of mass is Every second, the Sun converts about 600 million tons of hydrogen into 596 million tons of helium. The remaining 4 million tons of mass is converted to an amount of energy equal to 4 million tons times the speed of light cubed. converted to an amount of energy equal to 4 million tons times the speed of light. reabsorbed as molecular hydrogen. converted to an amount of energy equal to 4 million tons times the speed of light squared. ejected into space in a solar wind.

Answers

Answer:

Converted to an amount of energy equal to 4 million tons times the speed of light squared. ejected into space in a solar wind.

Explanation:

The 4 million tons of mass is converted to the amount of energy that is equal to 4 million tons times the speed of light squared. This energy moves from the sun with the help of solar winds and received by the planets present in the solar system. This solar energy moves in the form of solar radiation because there is no medium for propagation so that's why we can say that the mass is converted into energy that moves in the form of radiation in discrete packets.

can someone help me pls

Answers

Answer: food, female water

Explanation:

Can I have brainliest

Answer :  dog horse  cat lion deer  moose tiger cheetah hippopotamus zebra rabbit  penguin dolphin  shark fish

Explanation:

Cold packs are designed to become very cold when activated. When the pack is activated, a chemical reaction occurs to make the temperature of the cold pack decrease. What must be true of this chemical reaction? (2 points) The reaction releases energy to its surroundings. The reaction releases energy to its surroundings. The products and reactants have the same amount of energy. The products and reactants have the same amount of energy. The products have less energy than the reactants. The products have less energy than the reactants. The reaction absorbs energy from its surroundings.

Answers

Answer:

The reaction absorbs energy from its surroundings.

Explanation:

An endothermic reaction is any reaction in which energy is absorbed by the reaction system.Thus implies that energy is withdrawn from the environment A cold pack's function is based on an endothermic chemical reaction.

The absorption of energy by the reaction system means that the environment feels cool in an endothermic reaction.This manifests in a decrease in the temperature of the cold pack.

Which of these terms means an object's resistance to changing its motion?

Question 1 options:

inertia


velocity


newton


power

Question 2 (1 point)
Which of these equations is a representation of the 2nd Law of Motion?

Question 2 options:

v=d/t


W=Fd


F=ma


a=v/t

Question 3 (1 point)
Which words correctly complete the 3rd Law of Motion?

For every ___________ there is an equal and opposite ___________.

Question 3 options:

cause, effect


action, reaction


distance, velocity


cost, benefit

Question 4 (1 point)
Which of these could be a force that changes the motion of an object?

Question 4 options:

friction


a push or pull


air resistance


all of the above

Question 5 (1 point)
According to the second law of motion, which statement is TRUE?

Question 5 options:

every action has a reaction


a heavy object requires more force to push than a lighter object


an object at rest, stays at rest


heavy objects accelerate faster than lighter elements with the same force

Answers

Answer:

Inertia

F=ma

Action, reaction

All of the above

A heavy object requires more force to push than a lighter object.

No matter how well we get along with our parents as adolescents, there comes a time when we need to break away and assert our own independence. There are several ways in which we do this, some of them deliberate and intentional and some of them not so intentional. Describe several ways you use or have used to break away from your parents. Briefly describe your parents' reactions. ​

Answers

Answer: I never said anything to them but if i did it would be "I need a break from you, i love you but sometimes I have to find the path on my own." i would say this if i wasn't scared to hurt them.

Explanation:

define gravitational field intensity?​

Answers

Explanation:

The strength of the gravitational field is known as gravitational field intensity. It is the gravitational force acting on a unit test mass.

Which of the following is most likely to happen when a sound wave reflects
off a hard surface? (Assume that neither the source of the sound nor the hard
surface is moving.)
A. A beat frequency
B. An echo
O C. A change in speed
O D. A change in pitch
SUBMIT

Answers

Answer:

B. An echo

Explanation:

An echo is the sound heard after the reflection of sound waves from a hard surface. It has both advantages and disadvantages with respect to its applications.

Some of it applications include;

i. it can be used to determine the depth of the sea

ii. it can be used in crude oil exploration

iii. it can be used to determine the speed of sound in air

An echo is different to reverberation of sound.

(b) The cylinder shown in figure 2 is fitted with a freely sliding piston containing an ideal gas of mass 13g and volume 1.0×10⁴ cm⁵ . The tempreture of the gas is 25°C and it is initially at atmospheric pressure.

(i) The gas is heated to a Tempreture of 400°C . what is the new volume of the gas?​

Answers

Answer:

22600 cm³ (3 s.f.)

Explanation:

Please see the attached picture for the full solution.

A 15N block is sliding at constant speed across the frictionless floor of an ice rink.

Answers

Answer:

so, why we have to find here..

stay safe healthy and happy.

Below is a single strand of DNA, what is the complementary base pair for the strand?
AAG, GCA, TCA, GAT

Answers

The complementary base pair is:
TTC, CTG, AGT, CTA.

True or False: A higher vapor pressure (evaporates easily) corresponds to strong intermolecular forces. (dont answer)
anyways free p o i n ts...

Answers

Answer:

truuuuuuuuuuuuuuuuuuuuuuuuujuuuuuuuur

Answer:

true

Explanation:

I took a test this year and I know the answer

What is an important difference between nanotechnology and microtechnology?

Nanotechnology shows results of quantum mechanics, but microtechnology does not.
Microtechnology shows results of quantum mechanics, but nanotechnology does not.
Microtechnology is used to make products, but nanotechnology is not.
Nanotechnology is used to make products, but microtechnology is not.

Answers

Answer:

A) Nanotechnology shows results of quantum mechanics, but microtechnology does not.

Explanation:

Edge 21 test

The difference between nanotechnology and micro technology is nanotechnology shows results of quantum mechanics, but micro technology does not.

What are the differences between micro-technology and nanotechnology?

Micro technology:

      The technology that can be featured completely in a microscopic scale is known to be micro - technology. This technology that contribute to design, use components, devices that involves in small size. These were done significantly in smaller features.

Nanotechnology:

      Nanotechnology is the field of applied science and technology that can be measured through nanoscale. Nanotechnology is helping to considerably improve, industry sectors - information technology, homeland security, medicine, transportation, energy, food safety, and environmental science, among many others.

Thus, Nanotechnology shows results of quantum mechanics but micro-technology does not. Option A is the correct answer.

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What is a half-life?​

Answers

Answer:

When yo die early

Explanation:

Answer: A I think but I'm sure that Half Life is a video game by Valve.

Explanation:

Elena puts her eggs in a cage made out of wood. The wood breaks during
the landing, but the eggs survive. Which would be the best reason to
explain why this prevented her eggs from breaking?"
O Directs the energy of the impact towards the egg
O Decreases the velocity of the egg before it starts slowing down
O Increases the time that the egg slows down
O Decreases the time that the egg slows down.
O Directs the energy of the impact away from the egg
O Increases the velocity of the egg before it starts slowing down

Answers

Answer:

I think the answer is Decreases the time that the egg slows down.

Explanation:

If not try it starts slowing down

O Increases the time that the egg slows down.

Between which of the following surfaces would the force of friction be
greatest?
A. Rubber shoe soles on artificial turf
B. Rubber shoe soles on ice
C. Rubber shoe soles on asphalt
D. Rubber shoe soles on wet grass

Answers

C. Rubber shoe soles on asphalt


What is the direction of the force on a positive charge when passing through a magnetic field as indicated in this diagram? Explain how you got
your answer.

Answers

Answer:

The direction of the magnetic force on a moving charge is perpendicular to the plane formed by v and B and follows right hand rule–1 (RHR-1)

Explanation:

hope this helps

Answer:

The direction is into the page. Your thumb is along the velocity vector and your fingers travel along the magnetic-field vector to leave your palm moving into the page

Explanation:

Plato

A person can lands safely on the surface of the earth but not moon. why?​

Answers

Answer:

The gravitational force on the moon is less than on Earth, because the strength of gravity is determined by an objects' mass. The bigger the object, the bigger the gravitational force. Gravity is pretty much everywhere

Explanation:

Why might astronauts choose to “lope” or hop rather than walking or running on the moon? Astronauts can “lope” in the moon's low gravity levels, even though this gait pattern is very difficult to use on Earth.

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