concept

isotope

An isotope is an atom with the same number of protons but a different number of neutrons in its nucleus.
10 related articles · 1 formulas · 1 who worked here

Description

Isotopes are 'twin brothers' of chemical elements. They have the same number of protons but different numbers of neutrons, so they behave almost identically in chemistry but may have different masses. For example, all carbon atoms have 6 protons, but carbon-12 and carbon-14 are isotopes with 6 and 8 neutrons, respectively.

History

After the discovery of radioactivity by Becquerel in 1896, Ernest Rutherford and Frederick Soddy showed in 1902 that radioactive decay is accompanied by the transmutation of elements. In 1913, Soddy introduced the term 'isotope' for chemically indistinguishable radioelements with different masses. That same year, J.J. Thomson discovered neon isotopes of masses 20 and 22. The discovery of the neutron by James Chadwick in 1932 explained the existence of isotopes. Today, the study of isotopes underlies a multitude of methods: from radiocarbon dating to nuclear medicine.

How it works

The difference in neutron number leads to a difference in nuclear binding energy, which determines stability. According to the liquid drop model and the Weizsäcker formula, the binding energy depends on Z and A. Radioactive isotopes decay according to the radioactive decay law N(t)=N₀e^{-λt}. Mass spectroscopy allows separating isotopes by mass-to-charge ratio. Quantum effects such as tunneling explain α-decay. The Pauli principle governs the filling of nuclear shells, and neutron resonances play a role in neutron capture.

Fun fact

Carbon-14 helps archaeologists determine the age of ancient finds. It is radioactive and gradually decays, so by measuring how much remains, one can find out when the organism died.

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Formulas

$$t = \frac{1}{\lambda} \ln \left( \frac{N_0}{N} \right)$$
Time elapsed from initial to current isotope ratio.
What is in the formula
tvariableelapsed time — time second
λvariabledecay constant — decay constant per second
N_0variableinitial number of radioactive nuclei — number of nuclei
Nvariablecurrent number of radioactive nuclei — number of nuclei
lnoperatornatural logarithm of the ratio — natural logarithm
t=\frac{1}{λ}\ln(\frac{(^{26}{al}/^{27}{al})_0}{(^{26}{al}/^{27}{al})_{{sample}}}) · 2606.04529v1

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