Questions tagged [half-life]
Half-life is the time required for an attenuating quantity to reduce to half of its initial value. It is proportional to the mean lifetime, whose inverse is the decay constant. It is a constant for exponential decay.
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Why is the relaxation of coherence rate half the spontaneous emission rate?
Consider a two-level atom of which the lower and upper levels are denoted, respectively, a and b. If spontaneous emission from the upper to the lower level is the only source of relaxation, then the ...
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If the time at which a single atom decays is random, why do groups of atoms behave in predictable ways? [duplicate]
Why do groups of atoms decay at predictable rates even though a single atom’s decay point is completely unpredictable? I’m having trouble wrapping my head around this.
From my reading, it seems that ...
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Decay rate with specific helicity in rest frame and lab frame
Consider a two-body decay, such as the pion decay: $\pi^+\to \mu^+ + \nu_\mu^{}$. In the Standard Model, as there only exits left-handed massless neutrinos, the helicities of final particles are known....
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Difference between endpoints and kinetic energy in a beta minus decay
I want to understand the difference between the Q value and Endpoint energy and Kinetic energy of a beta minus decay.
I understood that the Q value is the overall energy of the reaction given by
Q ...
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How is rate of radioactive decay constant?
If I understand correctly, the rate of radioactive decay depends on the amount of the radioactive element. How then can it be constant, if it depends on concentration?
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Nuclear decay formula derivation
I don't understand why the nuclear decay formula is derived with logarithms.
if $t=T_{1/2}$ then
$N=N_0\cdot\frac{1}{2}$
if $t=2T_{1/2}$ then
$N=N_0\cdot\frac{1}{2^2}$
if $t=3T_{1/2}$ then
$N=N_0\cdot\...
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What is the half-life of deuterium if protons decay?
If we where to assume that protons decay and we know the half-life of protons, would it be possible to determine the half-life of deuterium?
If $^{1}$H (a single proton) has a half-life of, say, $10^{...
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What might be the half-life of observationally stable nuclei with energetically favorable decay modes?
For example, a reaction
$${}^{132} \mathrm{Ba} \rightarrow {}^{128}\mathrm{Xe} + \alpha + 22.19\mathrm{keV}$$
would be energetically favorable, contrary that ${}^{132} \mathrm{Ba}$ is observationally ...
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Where could I find an example of a numerical calculation in quantum electrodynamics?
I’ve been reading Student Friendly Quantum Field Theory and I’m discouraged by the fact that I’ve yet to encounter an actual numerical calculation in the book. I feel like I would be able to ...
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Radioactive decay: calculating probability of decay from half life/decay constant
Let's say due to a nuclear reaction a radionuclide of half-life $T_{1/2}$ was created. I am trying to find out what will be the probability of that radionuclide undergoing radioactive decay within ...
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Should I use Ground State-Ground State (GS-GS) $Q$-value for decay heat?
I am calculating the decay heat of sample of an isotope of plutonium at a single point in time. To do so, I am using the formula
$$Q = λNE,$$
where $Q$ is the decay heat for a given sample of ...
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Detection the age of fossils using the carbon dating method
The life of carbon-14 isotope is about 5 thousand years. But we still are able to detect traces of it in fossils which are older, more than 10 thousand years. Why?
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When can a sum of exponential decays be approximated by a single exponential decay?
In my experiment, I have a signal y(t) that should be given by a continuous sum of exponential decays:
$y(t) = \int_a^b n_0(E) \exp[-t/\tau(E)] {\rm d}E$
However, I see just a single exponential decay....
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Simulating $e^-\rightarrow e^-\gamma$ scattering in QED
Is there any physical reason/symmetry prohibiting me from studying the $e^-\rightarrow e^-\gamma$ interaction? Because I haven't seen any QFT textbook dealing with such a simple process. It is the ...
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Maximum and Minimum electron energy
I am trying to find the maximum and minimum electron energy for the calculation of the beta spectrum. I understood the minimum energy of the electron is the Q value. What is the maximum energy of the ...
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Equation to predict stability, half-life and decay products of atomic nuclei?
Given an atomic nuclei say C-14 or U-233 or anything in-between or outside the range and given the ratio of protons and neutrons in the nuclei, is there a comprehensive equation or set of equations ...
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Why is water bright in a T2 weighted image?
I am new to study MRI. Please understand if some terminologies I use are wrong.
This might be a silly question, but I wonder why water is bright in a T2 weighted image. T2 relaxation is also called ...
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Radioactive Decay of Li-8
Currently using a simulation to observe the decay of various elements. I noticed for the Li-8 there is beta decay. There are also arrows pointing from beta decay towards alpha decay and stable. Can ...
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Why does Americium-241 not exist naturally?
A few searches says that it's because "the half life is too short with respect to the age of the universe." I don't understand what that means.
Note that the half life of Americium-241 is ...
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Why is Astatine-210 (At-210) the longest-lived isotope of astatine despite possessing an odd number of neutrons?
I am guessing that isotopes with an even number of neutrons more readily release an alpha particle... When and if At-210 does that, it still has the problem of being 'odd/odd'...
But this begs the ...
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Isotopes half-lives distribution - is it log-uniform?
Decay of single isotope follows exponential law.
BUT decay of nuke fallout / spent nuclear fuel will follow hyperbolic law. It is easy to explain if we assume that half-lives are log-uniformly ...
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Relationship between reactivity and half lives
I understand that after the 4th half life, there will be $\frac{1}{16} = 0.0625$ of the original substance left but I'm not sure how to find the half life according to this graph (since it's not ...
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Why does the doubly-magic nucleus tin-$132$ have such a short mean lifetime?
Why does the doubly-magic nucleus tin-$132$ have such a short mean lifetime? Only because it is far from valley of stability?
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Does a charged isotope have a different half life than the neutral counterpart?
Let's say you have a radioactive isotope of an element with relatively short half-life (e.g. <0.5s).
If you add or remove electrons from the atom so that is has a positive or negative charge, is ...
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Lifetime derived from a measured spectrum when initial and final state have a finite lifetime
Can we infer the lifetime of states from a simple absorption or emission spectrum if both states involved in the transition have finite lifetimes? For example excited state absorption. It seems that ...
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Why is $\tau=1/k$ the time constant of an exponential decay $f(t)=e^{-kt}$
Some context on why I came up with this question:
I have to do a presentation on a paper about the heat equation on the cooling of a metal bar.
In this experiment, the general solution for the PDE is:
...
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Why do things decay in terms of base $e$?
For instance, why do radioactive elements follow some $e^{-x}$ relationship? Why not $\pi^{-y}$ or some other numerical constant as the base? Is there some fundamental reason for Euler's number ...
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Why is there a sudden drop-off in half-life of isotopes at around 130 neutrons? Is there a name for this?
Pertaining to the chart of nuclides, there is a region above Bismuth, in which the relatively continuous trend of stability is interrupted by a batch of isotopes all with extremely short half-lives. I ...
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How should half-lives be added?
Suppose I have a sample which can decay via two processes and/or decay to two separate products,
$$A \to B, A \to C$$
The total half life can be calculated $t= (t_A^{-1} + t_B^{-1})^{-1}. $
I am ...
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General Half-life calculation for an abitrary nucleus
I have been getting back into physics and I was wondering whether there was a generalized half-life equation for any given nucleus composition.
For instance for gold isotope 210-AU. Is it possible to ...
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What is the analogy of cross section for particle decays?
So if two particles are fired at each other the chance they interact is the cross section of the interaction. What is the equivalent term for the chance that a particle decays into certain particles? ...
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Conservation of energy with metastable pure states and doubts about energy-time uncertainty relation
Experimentally we know there are metastable states in nuclear physics and molecular physics. For example, the isotope Tantalum-180m ${}^{180m}\text{Ta}$ is long-lived metastable excited state, with a ...
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How do physicists know that some of a beta ray/particle's 'missing' energy isn't lost to interference with the electron cloud surrounding the atom?
Enrico Fermi and Wolfgang Pauli ultimately concluded that beta decay resulted in an electron and an electron antineutrino leaving a nucleus... BUT...
How does the electron leaving a neutron punch its ...
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Experimental results for the measurement of Positron lifetime / Positron decay [duplicate]
It is assumed that the positron, being the antimatter particle of the electron, is stable.
I am interested in finding experimental results or experiments which have measured the positron lifetime in a ...
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Why is radioactive half-life constant?
Say you have just four radioactive atoms with a half-life of one hour. (I am using a small number of atoms to keep it simple and illustrate my confusion more clearly). So that means one hour from now, ...
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What is the half-life of isotopes that decay via electron capture, if they are stripped of their electrons?
If an isotope that undergoes decay via electron capture, like 7Be, loses ONE electron, how will its radioactive half life change? What about 2 electrons? And so on and so forth for heavier elements? ...
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Calculation for Decay of a Pseudoscalar to Two Particles [closed]
I am following some of the exercises in Srednicki's textbook on QFT. One of the questions is to consider a theory with a real scalar field $\phi$ and a complex scalar field $\chi$ with
$$L=g \phi \...
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Energy as a function of half-life?
How much energy is released in the radioactive substance's decay of one cycle of its half life? I'd like the plot the energy released of a radioactive substance over time. What must I reference to ...
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Question on the life-time of a super-symmetric particle [duplicate]
I was watching a random video on SUSY. In the video, they were discussing that SUSY explains dark matter. That DM is probably a SUSY particle.
How is this possible? We know that the life of a Top ...
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Do unstable nuclei affect each other for decaying?
I am thinking about beta decay.
If we graph decayed nuclei count over time, we don't see a linear line. Rather, it would be a curved line.
I imagine myself as an unstable nucleus.
If I don't care ...
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How exactly Radiocarbon dating Works?
So how exactly does Carbon Dating work ?
$^{14}$C is produced from $^{14}$N in the atmosphere. Since there is considerable amount of Nitrogen in the atmosphere,we can have quantifiable amount of $^{14}...
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What determines the half-life (or stability) of an isotope?
Why is it that some elements do not have any stable isotopes, while others of very similar mass have multiple stable isotopes? What determines this phenomenon and what determines the strict ...
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Half-Life for Few Nuclei in a Sample
I read somewhere in some textbook that
"The concept of half life and mean half life becom meaningless ehen you have a sample containing only a few nuclei. For example, if you are given say, 100 ...
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Why mean life of radioactive element is slightly greater than halflife..? [duplicate]
I was reading radioactivity where I find that half life of a radioactive material is less than mean life due the presence of $\log2$ in the numerator:
$$ t_{1/2} = \frac{0.693}{\lambda} $$
But how ...
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Time constant versus half-life — when to use which?
In some systems we use half-life (like in radioactivity) which gives us time until a quantity changes by 50% — while in other instances (like in RC circuits) we use time constants. In both cases the ...
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How do I determine the half-life from a change in the activity of a sample over a known time?
If I know that the sample originally has an activity of $A_0$ and after a time $t$ has an activity of $A_1$, how can I use this to determine the half-life of the material?
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How Quickly Does an Atom Transfer From One Orbital to Another? [duplicate]
Here's the research that I've done:
The Schrödinger equation:
$$i\hbar\frac{\partial}{\partial t}|\psi(t)\rangle=\hat{H}|\psi(t)\rangle$$
Ok, it evolves as a function of time. That tells us something....
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How might one stop a radioactive agent from radiating?
Source
There have also been grim signs of things to come from the Russian government. A new national standard for “Urgent burial of corpses in peacetime and wartime” has been introduced by the ...
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Is there a way to reconstruct a "full-life" from a "half-life" of a decomposing piece of waste?
(please gently redirect me if it's a wrong SE and don't question-ban me, I mean no harm)
Paper products have a lag time of 1.5–2.0 years before methane production, a ‘half-life’
of 10–20 years, [...]
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Does Half life apply for all kinds of radioactive material?
Correct me if I am wrong, but for example when half of a sample U-235 undergoes alpha decay, it marks its half life. However, what if a sample undergoes gamma decay? Wouldn't its mass always stay the ...
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