Four years after publication of the Schrödinger equation, Lev Davidovich Landau, age 23, solved the equation for a charged particle moving in a uniform magnetic field. A single electron moving perpendicular to a field B can be considered as a model atom without a nucleus, or as the irreducible quantum limit of the cyclotron. Landau proved that its energy is quantized in uniform steps of eħB/me. Gerald Gabrielse traps a single electron in an evacuated centimeter-size metal can cooled to a temperature of 90 mK. In a magnetic field of magnitude 5.37 T, the electron circulates for hours in its lowest energy level, generating a measurable signal as it moves. Evaluate the size of a quantum jump in the electron's energy. State your answer to the nearest micro electron Volt (µeV).
Quantum mechanics and hydrogen atom
Consider an electron of mass m moves with the velocity v in a hydrogen atom. If an electron is at a distance r from the proton, then the potential energy function of the electron can be written as follows:
Isotopes of Hydrogen Atoms
To understand isotopes, it's easiest to learn the simplest system. Hydrogen, the most basic nucleus, has received a great deal of attention. Several of the results seen in more complex nuclei can be seen in hydrogen isotopes. An isotope is a nucleus of the same atomic number (Z) but a different atomic mass number (A). The number of neutrons present in the nucleus varies with respect to the isotope.
Mass of Hydrogen Atom
Hydrogen is one of the most fundamental elements on Earth which is colorless, odorless, and a flammable chemical substance. The representation of hydrogen in the periodic table is H. It is mostly found as a diatomic molecule as water H2O on earth. It is also known to be the lightest element and takes its place on Earth up to 0.14 %. There are three isotopes of hydrogen- protium, deuterium, and tritium. There is a huge abundance of Hydrogen molecules on the earth's surface. The hydrogen isotope tritium has its half-life equal to 12.32 years, through beta decay. In physics, the study of Hydrogen is fundamental.
i provided a solution for the same problem but while using 5.26 T instead of 5.37 T. In the solution provided it gives the answer in eV but for my question, i need the answer to be in micro electron Volt (μeV).
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