Calculation of the radioactive decay

The half-life of radon is 3.82 days. How long will it take for 60 percent of a sample of radon to decay?

[mineapple]

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[chinemelumnwankwo]

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[SuperGreatSphinx]

Radioactive decay (also known as nuclear decay, radioactivity or nuclear radiation) is the process by which an unstable atomic nucleus loses energy (in terms of mass in its rest frame) by emitting radiation, such as an alpha particle, beta particle with neutrino or only a neutrino in the case of electron capture, or a gamma ray or electron in the case of internal conversion.

A material containing such unstable nuclei is considered radioactive.

Certain highly excited short-lived nuclear states can decay through neutron emission, or more rarely, proton emission.

Radioactive decay is a stochastic (i.e. random) process at the level of single atoms.

According to quantum theory, it is impossible to predict when a particular atom will decay, regardless of how long the atom has existed.

However, for a collection of atoms, the collection's expected decay rate is characterized in terms of their measured decay constants or half-lives.

This is the basis of radiometric dating.

The half-lives of radioactive atoms have no known upper limit, spanning a time range of over 55 orders of magnitude, from nearly instantaneous to far longer than the age of the universe.

A radioactive nucleus with zero spin can have no defined orientation, and hence emits the total momentum of its decay products isotropically (all directions and without bias).

If there are multiple particles produced during a single decay, as in beta decay, their relative angular distribution, or spin directions may not be isotropic.

Decay products from a nucleus with spin may be distributed non-isotropically with respect to that spin direction, either because of an external influence such as an electromagnetic field, or because the nucleus was produced in a dynamic process that constrained the direction of its spin.

Such a parent process could be a previous decay, or a nuclear reaction.

The decaying nucleus is called the parent radionuclide (or parent radioisotope), and the process produces at least one daughter nuclide.

Except for gamma decay or internal conversion from a nuclear excited state, the decay is a nuclear transmutation resulting in a daughter containing a different number of protons or neutrons (or both).

When the number of protons changes, an atom of a different chemical element is created.

The first decay processes to be discovered were alpha decay, beta decay, and gamma decay.

Alpha decay occurs when the nucleus ejects an alpha particle (helium nucleus).

This is the most common process of emitting nucleons, but highly excited nuclei can eject single nucleons, or in the case of cluster decay, specific light nuclei of other elements.

Beta decay occurs in two ways: (i) beta-minus decay, when the nucleus emits an electron and an antineutrino in a process that changes a neutron to a proton, or (ii) beta-plus decay, when the nucleus emits a positron and a neutrino in a process that changes a proton to a neutron.

Highly excited neutron-rich nuclei, formed as the product of other types of decay, occasionally lose energy by way of neutron emission, resulting in a change from one isotope to another of the same element.

The nucleus may capture an orbiting electron, causing a proton to convert into a neutron in a process called electron capture.

All of these processes result in a well-defined nuclear transmutation.

By contrast, there are radioactive decay processes that do not result in a nuclear transmutation.

The energy of an excited nucleus may be emitted as a gamma ray in a process called gamma decay, or that energy may be lost when the nucleus interacts with an orbital electron causing its ejection from the atom, in a process called internal conversion.

Another type of radioactive decay results in products that vary, appearing as two or more "fragments" of the original nucleus with a range of possible masses.

This decay, called spontaneous fission, happens when a large unstable nucleus spontaneously splits into two (or occasionally three) smaller daughter nuclei, and generally leads to the emission of gamma rays, neutrons, or other particles from those products.

There are 28 naturally occurring chemical elements on Earth that are radioactive, consisting of 33 radionuclides (5 elements have 2 different radionuclides) that date before the time of formation of the solar system.

These 33 are known as primordial nuclides.

Well-known examples are uranium and thorium, but also included are naturally occurring long-lived radioisotopes, such as potassium-40.

Another 50 or so shorter-lived radionuclides, such as radium and radon, found on Earth, are the products of decay chains that began with the primordial nuclides, or are the product of ongoing cosmogenic processes, such as the production of carbon-14 from nitrogen-14 in the atmosphere by cosmic rays.

Radionuclides may also be produced artificially in particle accelerators or nuclear reactors, resulting in 650 of these with half-lives of over an hour, and several thousand more with even shorter half-lives.

[Mastergee-vywh]

Thanks alot bro I've been looking for this solving for so long I keep forgetting tnx so much

[karhukivi]

A lot of people get hung up on the half-life concept. It is just an easy way to make decay constants memorable - they are usually tiny numbers in units of inverse seconds - but it leads to questions like "how can anybody know the half life when it was thousands/millions of years ago" etc. This comes from not explaining exponential decay in terms of a steady rate proportional to the amount of atoms present. Far better to focus on the decay constant.

[chiyangiluwaili]

How do I find the dimensions for lambda using dimension analysis

[nursheraloon]

How came N value takes 40%? I don't get it.. Can u explain? 😊

[unsaali]

2:31 how is ans 5.05 days? I solved it with calculator but ans is 2.19 ...am I doing mistake somewhere? I am preparing for my entry test and this type of ques appeared in mock test and the worst thing is calculator is not allowed in test and there is no way I am gonna remember the log values ..