When an electron of an excited hydrogen atom descends, from an initial energy level (ni) to a lower (nf), characteristic electromagnetic radiation is emitted. The Bohr model of the H-atom allows the calculation of ΔE for any pair of energy levels. ΔE is related to the wavelength (λ) of the radiation according to Einstein's equation ( ΔE = [(hc)/λ]). Distinct series of spectral lines have been classified according to nf: Lyman series:nf=1 (91<λ<123 nm; near-UV). Balmer series:nf=2 (365<λ<658 nm; visible). Paschen series:nf=3 (819<λ<1877 nm; near-IR). Brackett series:nf=4 (1.456<λ<4.054 μm; short-to-mid-λ-IR) One of the lines in the emission spectrum of the hydrogen atom has a wavelength of λ = 2167 nm. A) Identify the value of nfinal . B) Identify the value of ninitial. (Answer as a whole number)
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.
When an electron of an excited hydrogen atom descends, from an initial energy level (ni) to a lower (nf), characteristic
| Lyman series:nf=1 (91<λ<123 nm; near-UV). |
| Balmer series:nf=2 (365<λ<658 nm; visible). |
| Paschen series:nf=3 (819<λ<1877 nm; near-IR). |
| Brackett series:nf=4 (1.456<λ<4.054 μm; short-to-mid-λ-IR) |
One of the lines in the emission spectrum of the hydrogen atom has a wavelength of λ = 2167 nm.
A) Identify the value of nfinal .
B) Identify the value of ninitial.
(Answer as a whole number)
Step by step
Solved in 3 steps
