The half-life of radium-226 is 1,600 years and the half-life of carbon-14 is 5,730 years. In 1-2 sentences, mathematically prove that the decay constant for radium-226 is larger than the decay constant for carbon-14.

Answers

Answer 1

The decay constant for radium-226 is larger than the decay constant for carbon-14 due to its obtained value.

What is the rate of decay?

The reduction in the number of radionuclides per unit time is the rate of decay.

The decay constant of the radium-226 is;

[tex]\lambda_1=\frac{ 16}{100}\times 266 \\\\ \lambda_1= -36.16[/tex]

The decay constant of the carbon-14 is;

[tex]\lambda_2=\frac{ -57.3}{100}\times 14 \\\\ \lambda_1= -802.2[/tex]

Hence, the decay constant for radium-226 is larger than the decay constant for carbon-14.

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Answer 2

Answer:

  0.693/1600 > 0.693/5730

Explanation:

The decay constant is the reciprocal of the time it takes for the radioactivity to decline to about 36.8% of its original value. It is the value of k in the multiplier e^(-kt), which tells the fraction remaining after time t.

When compared to the half-life, h, the value of k is ...

  k = 0.693/h . . . . . decay constant for half-life h

Effectively, the decay constant is proportional to the inverse of the half-life. The constant of proportionality is ln(2) ≈ 0.693.

__

decay constant for radium-226:

  0.693/1600 ≈ 4.33×10^-4

decay constant for carbon-14:

  0.693/5730 ≈ 1.21×10^-4

Since 4.33×10^-4 is greater than 1.21×10^-4, the decay constant of radium-226 is larger than that of carbon-14.

_____

Additional comment

Taking the reciprocal of a positive number reverses the ordering:

  1600 < 5730

  1/1600 > 1/5730

The half-life of radium-226 is less than that of carbon-14, so its decay constant will be larger.


Related Questions

a table tennis ball launcher fires a tennis ball. what do we know about the impulse on both of the objects?

Answers

Answer:

As we know by Newton's III law that if an action force is applied on an object then the reaction force of same magnitude in opposite direction will act on the other.

So here when ball is shot using launcher then the force will be same on launcher as well as ball so we can say

now since force is of same magnitude for both both then we will have

so from above we can say that both ball and launcher will have same impulse but opposite in direction.

Now since ball will have less mass so here it will have more speed while launcher is heavy in mass so its speed is slow or very small as comapre to ball.

This diagram shows a hydrogen atom. Explain why it looks
like it does

Answers

Answer:

Make-up of Hydrogen

Hydrogen atoms are extremely simple. They are the first atom on the periodic table, this means that they only have 1 proton. The majority of hydrogen atoms don't even have a neutron. As for electrons, hydrogen atoms with no charge have 1 electron. All of this means that for almost all hydrogen atoms the nucleus is made of one singular proton.

Diagram

The diagram shows a hydrogen atom. It looks like one circle because it is just showing the singular proton found in the nucleus. Electrons are extremely small compared to protons, so the electron is not shown in the picture. It is very hard to accurately depict electrons on diagrams like this because of their size and the fact that we can never know where they are. So, the diagram may look too simple but it just depicts how most hydrogen nuclei look.

Answer: It only has 1 proton.


a.5 kg model rocket launches with a thrust of 5 n in the upward direction. can it lift off of the ground? (hint: gravity is pulling it toward
the earth at 9.8 m/s2) (f=mx a) assume there is no wind resistance.

Answers

Answer:

F = F2 - F1     where F is the net force upwards

F = 5 - (.5 * 9.8) = (5 - 4.9) N = .1 N

Since there is a net force in the upwards direction the rocket should experience an upwards acceleration.

Does this equation show that transmutation has taken place during decay?
Why or why not?

6128 Ni -> 6128 Ni + y

A. Yes, because the numbers of nucleons and atoms are conserved.

B. No, because there is conservation of the number of atoms as well as the number of nucleons.

C. Yes, because the nickel atoms remain nickel atoms with the same number of neutrons.

D. No, because high-energy electromagnetic waves are emitted.

Answers

Explanation:

Transmutation means change in neutron numbers u

Like for example

When Potassium (N=19 ) goes through beta decay it forms (N=20)

Here no change in neutrons (Same 28)

So no trnasmutaions.

Option B

What are the functions of the respiratory system?

Answers

Answer:

- Allows you to talk and to smell.

- Warms air to match your body temperature and moisturizes it to the humidity level your body needs.

- Delivers oxygen to the cells in your body.

- Removes waste gases, including carbon dioxide, from the body when you exhale.

- Protects your airways from harmful substances and irritants

Describe how work done is related to a change in volume of a fluid. 100 points

Answers

Answer: work is the pressure acting through the change in volume

Explanation:

In the same way that work is defined as force operating over a distance,  work is the pressure acting through the change in volume.   Pressure is comparable to force in pressure–volume work, while volume is analogous to distance in the classic definition of work.

Just as we say that work force acting over a distance,for fluids,we can say that work is the pressure acting through the change in volume. for pressure- volume work, pressure is analogous to force, and the traditional defination of work.

Medium and heavy duty vehicles often require increased braking in situations where friction brakes overheat and fail. This can be addressed by using a(n):

Answers

Medium and heavy duty vehicles require a better braking option hence they ought to have an exhaust brake.

What is a brake?

A brake is used to slow down or stop an automobile. When the brake is applied, the speed of the automobile continues to decrease until it comes to a complete halt.

Friction brakes are apt for light vehicles that may not have the tendency to overheat. However, heavy duty vehicles may overheat often and do require an exhaust brake.The exhaust brake is most fitted for heavy duty vehicles and diesel engines.

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One evening, a student tells her sister that the Sun only appears brighter than other stars because the Sun and stars are different distances from Earth. Her sister disagrees, so the student supports her argument by asking her sister to observe the brightness of streetlights throughout their neighborhood. Which observation would support the student’s argument?

Answers

Comparing and analyzing the brightness of near and farther streetlight would support the student’s argument.

Which observation would support the student’s argument?

The brightness of nearer streetlight is more as compared to the brightness of the farther light because brightness decreases with the increase in distance.

So we can conclude that comparing and analyzing the brightness of near and farther streetlight would support the student’s argument.

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define scientific measurement​

Answers

Answer:

Measurements are a basic necessity in science. Scientists have designed thousands of different tools to help in the vital process of measuring. In this image of the control panel of the space shuttle Atlantis, we see dozens of readouts from measuring systems.

How are tardigrades related to astronomy?

A.
They live long enough to survive long space journeys.

B.
They are the only life form that requires no oxygen to survive.

C.
They can survive in extreme, harsh environments, including space.

D.
They are able to propel themselves in zero gravity environments.

Answers

Tardigrades related to astronomy as they can survive in extreme, harsh environments, including space for long time without oxygen.  The correct option is A , B and C.

What is tardigrades?

A special adaptation that allows the tiny animal known as the tardigrade to curl up into a dry, lifeless ball and survive for decades.

Tardigrades can undergo utter vacuum and intense pressures more than five times as in the deepest ocean. Temperatures up to 300F and as low as -458F is maintained.

They survive in space and for long time for about 10 days. They can live without water for decades.

Thus, the correct option is A , B and C.

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What can you say about the effort force needed to lift an object using an ideal lever with a force advantage greater than 1?

Select one:
a. The effort force is the same as the lifting force.
b. The effort force is less than the lifting force.
c. The effort force is greater than the lifting force.
d. You have to use the formula to calculate the effort force.

Answers

When the effort force needed to lift an object using an ideal lever with a force advantage greater than 1,  The effort force is less than the lifting force. The correct option is b.

What is force advantage?

Force is the mechanical physical quantity. The force advantage is equivalent to the mechanical advantage equal to the ratio of output to the input force.

The force advantage is

F.A = lifting force / effort force

When the effort force is greater, FA is less than 1. When FA is greater than 1, definitely, the effort force is less.

Thus, the effort force is less than the lifting force. The correct option is b.

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Drag force on a body increase with the increase in speed of the body.justify with one example from everyday experience

Answers

The drag force is the force that opposes the movement of a body through a fluid.

What is the drag force?

The drag force is the force that opposes the movement of a body through a fluid. This occurs in cases such as when a car is moving through air.

Owing to the fact that drag force tends to slow down vehicles when they move at higher speed, vehicles that are meant for racing are streamlined to reduce the drag force.

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6. What quantity does the gradient of the distance - time graph represent? Justify your answer.​

Answers

Answer:

speed

Explanation:

In a distance-time graph, the gradient of the line is equal to the speed of the object. The greater the gradient (and the steeper the line) the faster the object is moving.

Which best explains horatio’s error? magnetism is not produced by electric currents unless the wire is coiled. the magnetic field does not continually spread outward from the wire. the magnetic field is produced inside the wire, not outside of it. magnetism is only produced when a metal bar is placed near the wire.

Answers

What best explains Horatio’s error is the magnetic field does not continually spread outward from the wire. Option B. This is further explained below.

What is a Magnetic field?

Generally, a Magnetic field is simply defined as an area of magnetism that exists around a magnetic substance or a moving electric charge.

In conclusion, The magnetic field does not continuously expand outward from the wire, which best explains Horatio's miscalculation.

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Answer:

B

Explanation:

2. why did adding layers of paper help prevent the egg from breaking open rather than one thick layer with the same number of sheets?

Answers

The question requires the concept of impulse which is defined as From this formula we see that force is inversely proportional to the time. This means that more the time taken by a particle to hit the surface, lesser will be the force

how can electricity be stopped

Answers

Answer:

Insulators such as glass, mica, rubber or plastic used to coat metals and other conductors help stop or reduce the flow of electrical current. This helps prevent shock, fires, and short circuits.

Explanation:

Make the following conversion:


A) 60∘C into F

B)70∘C into K

C) 303∘K into C

D) 140∘F into C


If you don't know what I mean by C, F, K and ∘ it meaning is:

C- Celsius

F- Fahrenheit

K- kelvin
∘- degree sign

Answers

Answer:

Kelvin to Celsius: C = K - 273 (C = K - 273.15 if you want to

HELP ME ASAP PLEASE!!!!!
What is the wavelength of an infrared wave with a frequency of 4.0E14 Hz.

Answers

Answer:

f λ = c = 3.00E8      frequency * wavelength = speed of light

λ = c / f = 3.00E8 / 4.0E14 = 7.5E-7 m

Note 1 angstrom = 1.00E-10 m and 1 milli-micron = 1.00E-9 m

So the wavelength would be 7500 angstroms

The visible spectrum is 4000 A - 7000 A  or 400 - 700 milli-microns

derive a relation between critical angle and refractive index​

Answers

Answer:

At the critical angle the angle of refraction (outside the medium) is 90°

Ni sin θ = Na sin 90° = 1    assuming outside medium is air

sin θ = 1 / Ni            where Ni is the refractive of the medium involved

Prove that force canbe defined as rate of change in momentum

Answers

The force can be defined as rate of change in momentum because consists of the action of rotating or twisting a body around its axis of rotation (pole) through the application of a force.

What is the difference between moment and force?

The magnitude of the moment (M) is defined as the product of the magnitude of the force (F) and the distance (d) between the line of action of the force and the axis. The unit of moment of a force in the international system of units is N.m.

Torque, or moment of a force, is the tendency of a force to rotate a body on which it is applied. Torque is a vector perpendicular to the plane formed by the force and radius of rotation vectors.

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Match each space mission with the correct milestone.

1. first animal in space
Apollo 11
2. first person in space
Sputnik 2
3. first person on the moon
Salyut
4. first man-made object in space
Vostok 1
5. first American in space
Sputnik 1
6. first space station
Freedom 7

Answers

Matching each space mission with the correct milestone

First animal in space ____________ Sputnik 2first person in space ____________  Vostok 1first person on the moon _________  Apollo 11first man-made object in space ____  Sputnik 1first American in space __________   Freedom 7 first space station ______________ Salyut

Meaning of space mission

A space mission is a mission that takes an individual, animal, a thing or material out of earth using a spaceship. This mission is always carried out with a desire to find out more about the galaxy earth is a member of and to learn about other planets.

In conclusion, the list above is the accurate Matching of each space mission with the correct milestone.

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Answer:

See attachment below, Hope it helps!

Emotional elevation only occurs in animal kin groups. please select the best answer from the choices provided t f

Answers

Emotional elevation can occur in individuals or in groups, therefore, it is false that emotional elevation only occurs in animal kin groups.

What is emotional elevation?

Emotional elevation is the process whereby the moods of individuals are elevated due to their interactions with others or due to other factors.

Emotional elevation can occurs in individual animals or those on animal kin groups.

Therefore, it is false that emotional elevation only occurs in animal kin groups.

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Answer:

F

Explanation:

A length of wire is cut into 3 equal pieces. if each piece has a resistance of 0.20 , what is the resistance of the original length of wire?

Answers

Answer:

0.6

Explanation:

the original wire is three times the length there fore the longer the wire the more resistance

therefore the resistance of the original wire is 3 times greater making it 0.6

Explain how the wave behave as the Frequency changes using the characteristic described in

Answers

Let's find the relationship

[tex]\\ \rm\Rrightarrow E=h\nu[/tex]

[tex]\\ \rm\Rrightarrow \lambda=\dfrac{c}{\nu}[/tex]

So if frequency increases Energy of the wave increases and wavelength decreases and vice-versa

In the heat equation what does Q represent

Answers

The heat equation is Q = mcT


Q is the total amount of heat transferred to or from something.

Can you help me I’m struggling?

Answers

BC is the answer as the solid is now melting at that point

What is the role of pressure and dissolved gases in eruptions?.

Answers

Answer:

Explanation:

Magma contains dissolved gases, which provide the driving force that causes most volcanic eruptions. As magma rises towards the surface and pressure decreases, gases are released from the liquid portion of the magma (melt) and continue to travel upward, and are eventually released into the atmosphere.

Can someone please answer this, ill give you brainliest Would be very appreciated.

Answers

Answer:

Option D

Explanation:

The plant burning induces the rate of smokes It also releases carbon dioxide to air with additional to black smokes.As it's released to atmosphere the amount of CO_2 also increases.

Option D is correct

Which answer correctly describes the grey lines in this Hering illusion? (Optical Illusions Lesson)

A close-up of a fanDescription automatically generated with low confidence



Question 1 options:

The grey lines are bent.


The grey lines are straight.


The grey lines are curly.


The grey lines are a figment of my imagination.

Answers

Answer: The grey lines are bent.

Explanation: The grey lines are bent.

The answer that correctly describes the grey lines in this Hering illusion is "The grey lines are bent." Option A. This is further explained below

What is the Hering illusion?

The Hering Illusion is one of several illusions in which a major component of a basic line picture is obscured.

In conclusion, The statement for the grey lines in this Hering illusion is "The grey lines are twisted.".

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As you travel up into the mountains of the troposphere, increasing elevation,
the air pressure...
Oa. Decreases because the air gets more dense
O b. Decreases because the air gets less dense
Oc. Increases because the air gets more dense
Od. Increases because the air gets less dense

Answers

Answer:

OA

Explanation:

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