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.
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!
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...
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...
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this was a homework problem from Kilani High School
The half life of silicon 32 is $710$ years. If $10g$ are present now
how much will be present in $600$ yrs?
find out $k$ using
\$\begin{array}{rlll}
&A=A_0 e^{kt}
&
&(1)\\
\textsf{make }A=5
&5=10e^{k \cdot 710}
&
&(2)\\...
Summary: Hydrogen peroxide, H2O2, decomposes as per following reaction scheme:
H2O2(l) → H2O(l) + O2(g)
The concentration versus time data for the decomposition of hydrogen peroxide is given in Table 1.
i) Calculate the reaction rate constant, k, graphically, with the aid of Excel software...
I believe I use a formula such as $$n\frac{t}{T}$$ but am unsure I've never done one without a given amount of the sampleSo if I was to use this I would get 8/(divided by)2.67 = 2.99625468 rounded to either 3 or 2.997 But i don't think this is write because you need to use 1/2 in this...
How did they calculate the half life of xenon 124 to be longer than the age of the universe if they only observed one decay? Is there some way to estimate half life?
Homework Statement
A -> Products
The two half-lives are 34 minutes and 68 minutes respectively. Find the order of the reaction.
So I and my friends are having disagreements over whether this is first order or second order or not.
Homework Equations
For first order half-life, t = 0.693/k
For...
Homework Statement
You have 0.0625 grams of an unstable element and 0.9375 grams of the stable daughter product. How many half-lives has it undergone？
Homework Equations
N=No (1/2)^(t/(t1/2))
In which
N represents the final activity for a period of time
No is the original activity
t...
Homework Statement
A two litre sealed container is filled with air at atmospheric pressure. It is connected to a vacuum pump which can pump air at a flow rate that is proportional to the difference in pressure within the container to the pressure outside. This tells us that the pressure drops...
Homework Statement
" Independent measurements are taken on two identical radioactive samples. On the first radioactive sample, a radiation detection system measures N decays on a radioactive sample during a total period of T. On the second radioactive sample, a radiation detection system...
Let me start out by saying that I have no idea what I'm talking about. I graduated from Indiana University with a Bachelor's in Spanish, and I work as a Loan Review Specialist at a bank, which has NOTHING to do with my degree, and still yet nothing to do with this topic.
But lately, I've become...
I recently read about a beta decay isotope (Rhenium-187),whose half life was changed from 42 X 109 years to 33 years, just by stripping the nucleus of all it's electrons. Why does this allow for a faster decay, and does this apply to all beta decay nuclei, or just Rhenium 187?
Homework Statement
http://d2vlcm61l7u1fs.cloudfront.net/media%2Ff62%2Ff62b6919-e60f-405b-81fb-2323ceeb03ee%2FphpsL4bVl.png
Homework Equations
So I need that in micrograms tho. So 4402*10^-18/1000=4.4*10^-18kg. or 4.4*10^-12 micrograms
that stills say it's wrong tho.
Is anyone familiar with a way to determine the half-life of a protein from its melt temperature (Tm)? It seems like there ought to be some sort of correlation, be it theoretical or empirical.
Just curious , have there been any such circumstances in the history of this universe (i'm thinking close or near the big bang moment of hot dense plasma) or are there possible such a scenario even theoretically where the half lives of isotopes and elements change?
In other words for example...
oops this is a pre calc question
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the half life of silicon-32 is $710$ years.
If $10g$ are present now
how much will be present in 600 yrs?
to find out $k$ using
$$A=A_0 e^{kt}$$
$$\frac{1}{2}=e^{k \cdot 710}$$
$$\ln\left[\frac{1}{2}\right]=k\cdot710$$...
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...
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...
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...
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)...
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...
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...
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...
[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...
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...
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...
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...
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...
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...
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...
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...
"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...
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...
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?
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...
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...
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...
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...
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?
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...
Homework Statement
Basically, the problem asked for the half life of Thorium-232, given the initial mass and the rate of decay.
\begin{equation}
\frac{dN}{dt} = 4100 \frac{ \alpha }{s}
\end{equation}
initial mass = 1.0 gHomework Equations
\begin{equation} \frac{dN}{dt} = \lambda N...
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...
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...
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...
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...
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...
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...
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
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...