# What is Half life: Definition and 125 Discussions

Half-life (symbol t1⁄2) is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential or non-exponential decay. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life is doubling time.
The original term, half-life period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to half-life in the early 1950s. Rutherford applied the principle of a radioactive element's half-life to studies of age determination of rocks by measuring the decay period of radium to lead-206.
Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation. The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed.

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1. ### Half life of multi chain decays

I am not really too sure where to start with this one, I would guess that the half life of the graph is very similar to the half life of the X to Y step, but at the same time I am unsure of how I would prove it. Any tips or reading material? Thanks!
2. ### I Half life and radioactivity clarification

As I understand, half life's are where unstable nuclear isotopes Undergo radioactive decay, where they emmit either aplha beta or gamma during this decay. I'm looking for some clarification on whether when an atom undergoes decay, does it then change into another element/ isotope of an...
3. ### How does Cmax decrease over time in human body? Use half life?

I'm interested in chemistry but it's all new for me and I'm just starting out. I tried to do some calculations but got stuck... I was wondering, for example a supplement has the following values: Molar mass: 306.247 g mol-1 Tmax 2-4 hours Cmax 363.3 ng / ml Half life: 11.21 hours How do...

18. ### Half-Life & Constant Emission: Understand Why

Homework Statement A radioactive source emits alpha particles at a constant rate 3.5x10^6 s^-1. The particles are collected for a period of 40 days. BY reference to the half life of the source, suggest why it may be assumed that rate of emission of alpha particles remain constant?The Attempt at...
19. ### Half life - Calculate the length of time

Homework Statement A source having a half life of 5.27 years is calibrated and found to have an activity of 3.5*10^5 Bq.The uncertainty in the calibration is +- 2% Calculate the length of time in days after the calibration has been made for the stated activity to have a maximum possible error...
20. ### How do I use this equation? Estimating half-life of a decay

How should I go about using equation 8.18? Link can be found below. In the book, an example is used where Th-220 --> C-12 + Po-208 with a Q value of 32.1 MeV is used, and it is said to yield t1/2 = 2.3x106 but for the life of me I cannot reproduce this result. This is what I did: Going from...
21. ### Activity of 1 g of carbon if 1 in 10^12 atoms are carbon-14

Homework Statement Carbon-14 decays by β emission and has a half-life of 5570 years. What is the decay constant of carbon-14? What is the activity of 1 g of carbon if 1 in 1012 atoms are carbon-14? After what time will the activity per gram have fallen to 3 Bq? Homework Equations λt½ = ln(2)...
22. ### A Nuclear Stability Calculations

Are there equations that detail the stability of nuclei against beta decay? On a related point, I'm familiar with the chart that shows all the isotopes and their half-lives (with a good chunk undergoing beta decay), but I was wondering if that can be derived from first principles, just using the...
23. ### A Equivalence equation between cross section & half life?

Is there equivalence equation between cross section & half life? For beta decay, we usually use half life to describe how fast or slow the decay undergo. For nuclear reaction, we use cross section to describe the possibility of reaction. In a sense, they reflect the same root physics spirit. Is...
24. ### I What does it mean when they say half life of a neutron

My book says that a free neutron, unlike a free proton is unstable. It decays into proton, electron and a antineutrino, and has half life of about 1000s. I do not understand how a single particle can have something called half life. I am finding difficulty to think of a proton being reduced...
25. ### Calculating Half life Decay in an Open system

[Question] So I was thinking about Physics for some time and for the sake of curiosity I've came with this problem: Let's say we have a liquid flowing into a system with infinite space. The flow is constant ( F ) The liquid decays over time with a half life ( λ ) We're looking for the Total...
26. ### B Nuclear Decay with time (half-life,initial activity/ nuclei)

Hi! I just keep having a hard time looking for the formula stating the relationship between half life, the initial number of unstable nuclei and the initial activity, can someone help me on that ? To be more specific, here is a problem which can be solved using that formula: "A substance has a...
27. ### Rb-87 Half Life Calculation: 478 Bq/g

Homework Statement Specific Activity of a sample of rubidium chloride is 478 Bq per gram knowing that activity is coming from Rb-87, calculate the half life of radioisotope - Molar mass of the RbCl natural is 120.9256 gram - Isotope composition of natural Rb is 72.15% and 27.85% respectively...
28. ### Determine half life from gamma radiation

I'm working on a lab and the task is to determine the half life of an element studying the beta radiation or the gamma radiation (emitted from the daughter). I have all the data and I'm done with the beta part, that was pretty straight forward. I have no clue how to relate the gamma radiation to...
29. ### Solve Half-Life Problem: Find # Atoms Decaying in 12 Days

Alright so i have exams in a matter of days and stumbled upon this multiple choice question 7. A radioactive source has 1.6×10^20 atoms of a radioactive isotope, with a half-life of 3 days. How many atoms will decay in 12 days? A. 1.0×10^19 B. 1.2×10^20 C. 4.0×10^19 D. 1.5×10^20 So my first...
30. ### I Is there a tie between half life and energy of decay?

As we all know radioactive isotopes have different half lives and different decay energies. Is there any tie between how long or short the half life is and the amount of energy of decay? I know that it will be a rather complex problem, especially for alpha decay where the mass of the...
31. ### Question about the game of "Half Life" -- Resonances....

So just a fun thread/question about the game Half life, and one of the events that happen in the game called a Resonance cascade. In the game, a Resonance Cascade is basically a "quantum event" where the crystal resonates at a certain frequency, causing other particles to resonate, cascading...
32. ### The Truth About Half-Life and Interest Rates

So I'm getting ready to buy some Tritium gun sights that will glow in the dark. The advertisement says Tritium has a half life of 12.3 so the sights will be about half as bright (50%) after 12.3 years. I'm wondering how bright they will be after 6 years and 2 months...will they be one quarter...
33. ### MHB What is the decay constant of tritium?

"Tritium is the basic fuel of hydrogen bombs and is used to increase the power for fission bombs . . . In a basic atom bomb (or reactor), plutonium atoms are split, or fissioned, to release energy, but the fission can be promoted with a small amount of tritium because it has two extra...
34. ### How Does Uranium Decay Impact the Temperature of Surrounding Lead?

1. The Lead is the final decay product of uranium-238 (half life = 4.7 billion years), so often the uranium is embedded in lead. The decay of 1.00 g of uranium to thorium converts 6.83x10-8 kg of mass to energy. Assuming the uranium absorbs none of the heat, what would be the...
35. ### Radioactive Isotopes and half life

Homework Statement If a radioactive isotope ends with 55.5 g, and has a half-life of 2.5 days, how much was there 8.3 days ago? Homework Equations mf=mi(1/2^t/h) The Attempt at a Solution the answer i got was 554 g, is it correct?
36. ### Calculating half life from experimental data

Homework Statement Decay of Carbon-11 from given data of count rate at time 0 to count rate at time 14 minutes in 2 minute intervals. Homework Equations I feel like I've gone wrong here because the answer I get of 19.6 minutes is actually negative if I go back and do the last equation again. I...
37. ### Half life and percentage remaining

Homework Statement 137Cs has a half life t1/2 = 30.07 years. After 50 years, what fraction of 137Cs will remain? Homework Equations maybe... dN/dλ = λN λ = ln2/t1/2, half life in seconds N = Total mass /(137(1.67x10-17kg)) The Attempt at a Solution i thought maybe i needed to figure out a...
38. ### Radioactive decay, need to find half life

Homework Statement The number of radioactive nuclei in a particular sample decreases over a period of 26 days to one-fifteenth of the original number. What is the half-life of the radioactive material, in days? Homework Equations R=DN/Dt=(lambda)(N)=(N)(ln2/T1/2) The Attempt at a Solution...
39. ### Find area under a decay curve if half life is increasing

Area under decay curve exp(-0.6969t/h) where t is the time (with t=0 initially) and h is a constant "half life" is analytically integrable, but what if the half life is increasing with time? I. e. if h(t) = H + at. (Note exp(-0.6969) is not exactly 0.5 but close and easy to remember.) This...
40. ### Two atoms of an element with a half life of ten years

On the other hand, what if we only have two atoms of an element with a half life of ten years. Then after then years, only one atom of that original element remains. What happens next? Is the lone surviving atom immutable?
41. ### Carbon-14 Half-Life: Calculating Decays After 50,000 Years

Homework Statement A sample containing carbon-14 has 16000 decays per minute. If the half life of carbon-14 is 5730 years. Aproximately how many decays per minute would be occurring after another 50 000 years. Answer: approximately 40 decays per minute. Homework Equations N= No x e^-λt...
42. ### How Do You Calculate the Half-Life of Thorium-232?

Homework Statement Basically, the problem asked for the half life of Thorium-232, given the initial mass and the rate of decay. $$\frac{dN}{dt} = 4100 \frac{ \alpha }{s}$$ initial mass = 1.0 gHomework Equations \frac{dN}{dt} = \lambda N...
43. ### How Long Should Radiation Therapy Last After Two Years to Match Initial Dosage?

Homework Statement a patient who is undergoing cancer theraphy is given 10 mins of irradiation from a radioactive source that has half life = 2 years. If the same source is to be used for same treatment 2 years later , how long should the patient should be irradiated? the ans is 20 mins .. can...
44. ### Half life and decay differential EQ problem

Homework Statement The Shroud of Turin, which shows the negative image of the body of a man who appears to have been crucified, is believed by many to be the burial shroud of Jesus of Nazareth. See the figure below. In 1988 the Vatican granted permission to have the shroud carbon-dated. Three...
45. ### MHB Half Life and Exponential Growth Question

Hey guys, I need help with a few more questions for this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. Question: For the first one, I took v(t) as 0 since that is when it would be stopping or changing directions. Then I solved for t to get...
46. ### Calculating Ozone Levels in a Room Using the Half-Life Equation

Just recently I decided to buy an ozone generator that can produce 4 grams of ozone / hour. However, I did a little research and found that ozone has a half life of 12.5 hours at 35 Celsius. For fun, I decided to find an equation that would let me know the amount of ozone left in the room...
47. ### Determining Half-Life of Element X from Gamma Spectrum: Tips and Challenges

Hello, I have a gamma spectrum of one element (X). There are several gamma peak in the spectrum. For example, 800 keV peak, 1000 keV peak and 1200 keV. I have an information about the peak area changing with time. Namely, I know the peak area in different times. So I can calculate the...
48. ### Exponential decay and half life problem

the half life of C14 is 5730 years. if a sample of C14 has a mass of 20 micrograms at time t = 0, how much is left after 2000 years? I learned from somewhere that these exponential decay and half life problems use the equation y = ab^t or y = a(1+r)^t where y = total, a = initial...
49. ### Derive relationship between radioactive constant and half life

Hi, I was wondering how to derive relationship between radiocative constant and half life, which is t1/2=ln2/b, where b=decay constant. It seemed like the it was just replaced into the equation A=A0(1/2)t/t1/2. Thanks in advance
50. ### Half life Tc-99m injected into a patient

Homework Statement A patient comes into the hospital for a bone scan and is injected with a dye containing Tc-99m. The half-life of Tc-99m is 6.03 h. What fraction of the original technetium will remain the patient 36 h after the procedure if radioactive decay is the only means by which it is...