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A sample contains radioactive atoms of two types, A andB.Initially there are three times asmany A atoms as there are Batoms. Two hours later, the numbers ofthe two atoms are equal. Thehalf-life of A is 0.72 hours. What is the half-life ofB?
I know how to solve decay rates for individual atoms but Iamlost as to how to solve this problem.

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Nestor Rutherford
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13 Mar 2019

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Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

I am stuck on this problem for three hours now.

It was found that a 30 gram mass hanging from a particular springhad an oscillation period of 1.7 seconds.

(a) When two 30 gram masses are hung from this spring, what wouldyou predict for the period in seconds?
New period with two masses = ? s

(b) When one 30 gram mass is supported by two of these vertical,parallel springs (see figure), what would you predict for theperiod in seconds?
New period with two springs = ? s

(c) Suppose that you cut one spring into two equal lengths, and youhang one 30 gram mass from one of these half springs. What wouldyou predict for the period in seconds?
New period with half spring = ? s

(d) Suppose that you take a single (full-length) spring and asingle 30 gram mass to the Moon and watch the system oscillatevertically there. What would you predict for the approximate periodin seconds? (The gravitational field strength on the Moon is aboutone-sixth that on the Earth.)
New period on the Moon = ? s

I found part a to be 2.4 secs. I just need to know how to do partb, c, and d. If you can help me and show me the steps, I willapreciate it!

A nuclear reaction is represented by an equation similar to theequation for a chemical reaction. An example of a nuclear reactionis the decay of radium into radon by the emission of an alphaparticle (a helium nucleus). The equation for this reactionis

^{226}_{\ 88}{\rm Ra}\; \rightarrow \, ^{222}_{\ 86}{\rmRn}+\;^4_2{\rm He}.

The superscript preceding each element indicates the nucleon numberof that particular nucleus (total number of protons and neutrons).The subscript indicates the charge of the nucleus, which is equalto the atomic number for nuclei. Nuclear reactions frequentlyinvolve electrons (sometimes called beta rays) and photons(sometimes called gamma rays). Electrons, which have nucleon number0 and charge -1, are represented in equations as either ^{\ \;0}_{-1}\beta or ^{\ \; 0}_{-1}{\rm e}. Photons are represented as^{0}_{0}\gamma to emphasize that they have no nucleon number andcarry no charge.

In nuclear reactions, several conservation laws are usuallysufficient to determine the products or reactants. One of these isconservation of nucleon number. The total number of neutrons andprotons in all of the reactants must be the same as the totalnumber of protons and neutrons in the products. Although protonsand neutrons sometimes change into one another, neither can simplydisappear. Another important conservation law is conservation ofcharge. The net charge of the reactants must be the same as that ofthe products.

Notice that, in our equation for the decay of radium, the sum ofthe nucleon numbers on each side is 226 and the sum of the chargeson each side is 88. If you knew everything in this equation exceptthe isotope of radon produced, you could simply subtract 4 from 226to find the nucleon number required to make the nucleon number ofthe products equal the nucleon number of the reactants. Similarly,if you knew everything in this equation except for the identity ofthe product element, you could simply subtract 2 from 88 and thenlook in a periodic table to find that the element with atomicnumber 86 is radon.

In parts A and B consider the decay of radon by alpha particleemission:

^{222}_{\ 86}{\rm Rn}\;\rightarrow\;X +\,^{4}_{2}{\rm He}.

a. What is the nucleon number of the element X?
Express your answer as an integer.

b. What is the atomic number (nuclear charge) of the elementX?
Express your answer as an integer.

n parts C and D consider the decay of Potassium-43 into calcium-43via the following reaction:

^{43}_{19}{\rm K} \rightarrow ^{43}_{20}{\rm Ca}+\,X.

c. What is the charge of the emitted particle X?
d. is not visible yet

E. An isotope of potassium with a half-life of roughly one billionyears is often used in radioactive dating. This isotope decaysthrough electron capture, the process of drawing an electron intothe nucleus. What is the chemical symbol for the element thatresults from this process? The equation for the reaction is

^{40}_{19}{\rm K}+\,^{\ \;0}_{-1}{\rm e}\rightarrow \,?.
Express your answer as a chemical symbol (e.g., Na forsodium).

f. The reaction energy of a reaction is the amount of energyreleased by the reaction. It is found by determining the differencein mass between the reactants and products and then using E=mc^2 toconvert the lost mass into the released energy.

Look again at the equation for the decay of radium (Ra), given inthe introduction. Use the following table of masses to determinethe reaction energy of this reaction.
Nucleus or particle Mass in atomic mass units
radium-226 226.025402
radon-222 222.017571
alpha particle 4.002602
Express your answer in joules to three significant figures.

please answer fully... thank you

In order to solve the problem you must refer to the first partwhich i already solved and I am 200% sure of the answers, however Iam stuck on the second part and I need help asap. Please do not getscared when you look at this problem and thank you soo much inadvance.

A wheel 75 meters in diameter is mounted vertically on an infinitefrictionless plane at the origin. The infinite frictionless planehas a grid of Cartesian coordinates on it. The moment of inertia ofthe wheel is mr^2. The mass of the wheel is 2000kg. There is anengine connected to the wheel that can produce a torque of 2.34x10^6 Nm. There is a 50 kg object attached to the circumference ofthe wheel that is attached to the wheel with a remote releasemechanism. The wheel is placed on the origin so that the plane ofthe wheel contains the point x=50 meters and y=86.8 m. The wheel ispositioned so that the object is just above the plane at the 6o'clock position. The engine is engaged and begins to apply thetorque to the wheel at 12:00 noon on March 1, 2011. The wheelbegins to rotate in the counterclockwise direction. The torque isapplied for 4 x 10^4 revolutions. At that point the object isreleased from the wheel and a 75 Newton motor accelerates theobject in the direction it is released. The motor is fired for 2.34x 10^4 seconds. (the following questions i have already answered)What is the angular velocity and rotational KE of the object justbefore it is released? (answer for that is 6.39 x 10^2 rad/sec and5.89 x 10^11 J). What angle does the path of the object make withthe x axis? (answer is 60.05 degrees). Where is the object on theinfinite frictionless plane when the motor stops (what are itscoordinates....answer is x=4.85x10^8m y=8.40x10^8m). What is thevelocity and linear KE of the object when the motor stops?(5.91x10^4 m/sec and KE= 8.73 x 10^10J). How much work was done onthe object up until the time the motor stopped? (8.73 x 10^10J).(Hint: the mass of the wheel is 2050 kg while the torque is appliedand the object is attached).

YEA I know what you are thinking at this moment. Difficult right?Please give it a chance and have faith in yourself. Here is thepart I had difficulty with:

After the engine stops firing the object is turned around so thatthe engine can be used to stop the object. The motor is fired atits rated thrust to stop the object. Unfortunately it malfunctionsand shuts down after an hour and the object coasts from then on. Atthe end of an hour of coasting it encounters a ramp that is 2000meters high and slopes up at an angle of 20 degrees. The objectclimbs the ramp and flies off the ramp into the air when it reachesthe end of the ramp. It strikes the plane and digs a crater 5meters deep in the plane and comes to a stop. How far from the endof the ramp does it land? Where does it land on the plane (as incoordinates)? What is the resultant velocity of the object and whatis the acute angle of the resultant velocity with the plane when itstrikes the plane? What is the KE of the object when it hits theplane? What date and time is it when the object lands on the plane?How much work was done on the object to stop it? How long did ittake to stop? What was the deceleration of the object in m/sec^2?What was the force on the object in Newtons to stop it?

If you are from MIT I have faith that you can do this. I am only ajunior in high school taking first year physics that is not evenAP. My teacher is from MIT and said he did this kind of stuff whenhe was there. Please please please help me! I'm desperate.

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