Learning Goal: To understand the Bohr model of the hydrogen atom. n 1913 Niels Bohr formulated a method of calculating the different energy levels of the hydrogen atom. He did this by combining both Classical and quantum ideas. In this problem, we go hrough the steps needed to understand the Bohr model of the atom. Part A Consider an electron with charge -e and mass m orbiting in a circle around a hydrogen nucleus (a single proton) with charge +e. In the classical model, the electron orbits around the nucleus, being held in orbit by the electromagnetic interaction between itself and the protons in the nucleus, much like planets orbit around the sun, being held in orbit by their gravitational interaction. When the electron is in a circular orbit, it must meet the condition for circular motion: The magnitude of the net force toward the center, Fe, is equal to mv²/r. Given these two pieces of information, deduce the velocity of the electron as it orbits around the nucleus. Express your answer in terms of e, m, r, and €0, the permittivity of free space. ▸ View Available Hint(s) v= 15| ΑΣΦ 1 πενη e 2 ?
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.
Please help with problem A
![Learning Goal:
To understand the Bohr model of the hydrogen
atom.
In 1913 Niels Bohr formulated a method of
calculating the different energy levels of the
hydrogen atom. He did this by combining both
classical and quantum ideas. In this problem, we go
through the steps needed to understand the Bohr
model of the atom.
Part A
Consider an electron with charge -e and mass m orbiting in a circle around a hydrogen nucleus (a
single proton) with charge +e. In the classical model, the electron orbits around the nucleus, being
held in orbit by the electromagnetic interaction between itself and the protons in the nucleus, much
like planets orbit around the sun, being held in orbit by their gravitational interaction. When the
electron is in a circular orbit, it must meet the condition for circular motion: The magnitude of the net
force toward the center, F, is equal to mv²/r. Given these two pieces of information, deduce the
velocity v of the electron as it orbits around the nucleus.
Express your answer in terms of e, m, r, and eo, the permittivity of free space.
► View Available Hint(s)
v=
[5] ΑΣΦ
1
πεπη
e
Submit
Previous Answers
?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34828ee0-4ec4-4963-9794-d063709fbf61%2Fb67e6a35-0a0c-4414-a8ae-eb6089a5e675%2F911wn7n_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
