An electron (restricted to one dimension) is trapped between two rigid walls 1.26 nm apart. The electron's energy is approximately 24 eV. a) What is the quantum number n for the energy state that the electron occupies? b) Based on the quantum number you found in part (a), calculate a more precise value for the electron's energy (in eV), expressed to at least three significant figures. (Use any physical constants or unit conversions to at least four significant figures in your calculations.)
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.
An electron (restricted to one dimension) is trapped between two rigid walls 1.26 nm apart. The electron's energy is approximately 24 eV.
a) What is the quantum number n for the energy state that the electron occupies?
b) Based on the quantum number you found in part (a), calculate a more precise value for the electron's energy (in eV), expressed to at least three significant figures. (Use any physical constants or unit conversions to at least four significant figures in your calculations.)
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