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.
1) What is expected of this experiment?
2) What would the outcome of this experiment be?
![Objective:
The purpose of this experiment is to practice the addition of vectors graphically and
analytically and to compare the results obtained by these two methods.
Apparatus:
ADDITION OF FORCES AND VECTORS
Cenco force table with pulleys, metal ring, string, mass hangers, masses, ruler, protractor
The force table provides a means for applying known forces at one or more points and in
various directions in the horizontal plane. The forces are the tensions in strings which
pass over pulleys attached to the rim of the circular table and from which masses are
hung.
Terminology:
3
Objects called "weights" have both a mass measured in kilograms (or grams) and a weight
measured in Newtons (or pounds). Weight is a measure of force (W = mg), NOT a
measurement of mass. In the SI (metric) system, weights are sometimes designated by
their mass. For example, a 100 gram "weight" is referred to by its mass of 100 grams.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c77c8ca-cf2a-49c8-86aa-e4a7d9346a8b%2F9f1457ef-b5c9-4262-9a42-d72bff2a977f%2Fwh8kf7c_processed.png&w=3840&q=75)
![Theory:
Pro
If several forces act on a body, the vector sum of these forces governs the motion of the
body. According to Newton's 1st Law of Motion the body will remain at rest (if originally
at rest) or will move with a constant velocity (if originally in motion) if the vector sum of
all forces acting on it is zero (the vector sum is called the resultant force). The body is
then said to be in translational equilibrium.
In this experiment, we consider forces acting on a small body (a metal ring), arranging
them so that the body is in translational equilibrium, and we determine how nearly these
forces satisfy the translational equilibrium condition that their vector sum is zero. Forces
will be measured in units called "gram-weight" (gmwt). One gmwt is the force of gravity
on one gram of mass. Therefore a mass of M grams will correspond to a force of M gmwt.
Ask your Instructor to discuss this further if you are still confused.
dure:
Note the strings already tied to the small ring at the center of the table. Clamp the pulleys
at not-too-symmetrical angles (otherwise the case becomes trivial). Placing one of the
pulleys at the 0° mark of the force table may be helpful to you but it is not necessary. Add
weights to the hanger at the end of each string and adjust the position of the pulleys if
necessary until the ring comes to rest at the exact center of the table. Tap or jiggle the
force table to reduce the effect of friction on the pulleys. Since the strings are radial from
the center of the force table (especially if the pulleys are properly aligned) the direction
of the forces may be read directly from the degree scale of the table.
Record the angular position of the pulleys and the weight hanging from each string.
(Remember to include the hanger weight in the overall weight.)
Determination of the Resultant Force:
Determine the vector sum of the horizontal forces acting on the ring in two ways:
graphically, and analytically, i.e. by summing trigonometric components. (In the following
discussion vectors are shown in boldface letters.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c77c8ca-cf2a-49c8-86aa-e4a7d9346a8b%2F9f1457ef-b5c9-4262-9a42-d72bff2a977f%2Fqwnhd6ub_processed.png&w=3840&q=75)
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