The wavelength (2) of matter waves may depend upon Planck's constant (h), mass (m) and velocity (v) of the particle. Use the dimensional analysis to derive the dimensional formula for 2. Hint: [h]=ML²T-¹
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.
![Activity 2:
The wavelength (2) of matter waves may depend upon Planck's constant (h), mass (m) and velocity (v) of the
particle. Use the dimensional analysis to derive the dimensional formula for 2. Hint: [h]=ML²T-¹
Activity 3:
A) Part of your work is to understand the different wire sizes and their power ratings. A certain kit contains
wires that belong to 9 categories according to their cross-sectional area, and their areas range from
0.1 mm² to 0.596 mm². If the area values of those categories form a geometric progression, write the
general formula of this progression, and the area of the first 3 categories.
B) The maintenance engineer for a certain supplier charges the factory for his/her services according to the
following: the first-hour costs 20 JDs; the second-hour costs 18.25 JDs (i.e., 1.75 JDs less than the
previous hour). This sequence of reduction in payment remains as more service hours are spent. Write
down the formula that describes the payment per hour, then calculate the payments for the first five
hours.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F647662e0-6cf9-429d-88eb-14c76b0ed44c%2F62bf3b8f-db0b-41b3-987d-a22cb7612577%2Ffr4bqx9_processed.jpeg&w=3840&q=75)
Step by step
Solved in 3 steps
