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→Exponential decay and half-life: Changed log to ln to remove ambiguity of base and added a hyphen for Beryllium-7
Specifically, the formula for the fraction of substance remaining after time t is:
Specifically, the formula for the fraction of substance remaining after time t is:
::<math>e^{-\frac{log(2)}{H}\ t}</math>
::<math>e^{-\frac{ln(2)}{H}\ t}</math>
where H is the half-life.
where H is the half-life.
While the mechanisms for decay, and hence the half-lives of various isotopes, are well understood on theoretical grounds, the calculations are so complex that half-lives are measured experimentally. The measured half-lives of the various isotopes of elements are known to be fixed quite accurately. Careful astronomical observations show that half-lives have not changed significantly in billions of years—spectral lines from distant galaxies would have shifted perceptibly if the constants involved had changed. In some cases radioactive decay itself can be observed and measured in distant galaxies when a supernova explodes and ejects radioactive nuclei.
While the mechanisms for decay, and hence the half-lives of various isotopes, are well understood on theoretical grounds, the calculations are so complex that half-lives are measured experimentally. The measured half-lives of the various isotopes of elements are known to be fixed quite accurately. Careful astronomical observations show that half-lives have not changed significantly in billions of years—spectral lines from distant galaxies would have shifted perceptibly if the constants involved had changed. In some cases radioactive decay itself can be observed and measured in distant galaxies when a supernova explodes and ejects radioactive nuclei.
The fundamental physical principles underlying radioactive decay are quite precise and based on quantum mechanics, but the overall decay rate of a given sample is subject to slight dependence on external conditions. These conditions involve the electric field in the vicinity of the nucleus, and are the result of the influence of the atom's electron cloud. The electron cloud is relatively very far away (a factor of many millions) from the nucleus, so the effects on the rate of radioactivity are tiny. The largest known effect that can be achieved without a particle accelerator or similar apparatus is about 1.5%, for the beta decay of Beryllium 7. See [[systematics of beta decay]] for details.
The fundamental physical principles underlying radioactive decay are quite precise and based on quantum mechanics, but the overall decay rate of a given sample is subject to slight dependence on external conditions. These conditions involve the electric field in the vicinity of the nucleus, and are the result of the influence of the atom's electron cloud. The electron cloud is relatively very far away (a factor of many millions) from the nucleus, so the effects on the rate of radioactivity are tiny. The largest known effect that can be achieved without a particle accelerator or similar apparatus is about 1.5%, for the beta decay of Beryllium-7. See [[systematics of beta decay]] for details.
==Antiquated notions==
==Antiquated notions==