# 6.2 The bohr model  (Page 4/9)

 Page 4 / 9

## Calculating the energy and wavelength of electron transitions in a one–electron (bohr) system

What is the energy (in joules) and the wavelength (in meters) of the line in the spectrum of hydrogen that represents the movement of an electron from Bohr orbit with n = 4 to the orbit with n = 6? In what part of the electromagnetic spectrum do we find this radiation?

## Solution

In this case, the electron starts out with n = 4, so n 1 = 4. It comes to rest in the n = 6 orbit, so n 2 = 6. The difference in energy between the two states is given by this expression:

$\text{Δ}E={E}_{1}-{E}_{2}=2.179\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-18}\left(\phantom{\rule{0.2em}{0ex}}\frac{1}{{n}_{1}^{2}}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{1}{{n}_{2}^{2}}\phantom{\rule{0.2em}{0ex}}\right)$
$\text{Δ}E=2.179\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-18}\left(\phantom{\rule{0.2em}{0ex}}\frac{1}{{4}^{2}}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{1}{{6}^{2}}\phantom{\rule{0.2em}{0ex}}\right)\phantom{\rule{0.2em}{0ex}}\text{J}$
$\text{Δ}E=2.179\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-18}\left(\phantom{\rule{0.2em}{0ex}}\frac{1}{16}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{1}{36}\phantom{\rule{0.2em}{0ex}}\right)\phantom{\rule{0.2em}{0ex}}\text{J}$
$\text{Δ}E=7.566\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-20}\phantom{\rule{0.2em}{0ex}}\text{J}$

This energy difference is positive, indicating a photon enters the system (is absorbed) to excite the electron from the n = 4 orbit up to the n = 6 orbit. The wavelength of a photon with this energy is found by the expression $E\text{=}\phantom{\rule{0.2em}{0ex}}\frac{hc}{\lambda }.$ Rearrangement gives:

$\lambda =\phantom{\rule{0.2em}{0ex}}\frac{hc}{E}$
$\begin{array}{}\\ \\ =\left(6.626\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-34}\phantom{\rule{0.2em}{0ex}}\overline{)\text{J}}\phantom{\rule{0.2em}{0ex}}\overline{)\text{s}}\right)\phantom{\rule{0.4em}{0ex}}×\phantom{\rule{0.3em}{0ex}}\frac{2.998\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{8}\phantom{\rule{0.2em}{0ex}}\text{m}\phantom{\rule{0.2em}{0ex}}{\overline{)\text{s}}}^{-1}}{7.566\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-20}\phantom{\rule{0.2em}{0ex}}\overline{)\text{J}}}\phantom{\rule{0.2em}{0ex}}\\ =2.626\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-6}\phantom{\rule{0.2em}{0ex}}\text{m}\end{array}$

From [link] , we can see that this wavelength is found in the infrared portion of the electromagnetic spectrum.

What is the energy in joules and the wavelength in meters of the photon produced when an electron falls from the n = 5 to the n = 3 level in a He + ion ( Z = 2 for He + )?

6.198 $×$ 10 –19 J; 3.205 $×$ 10 −7 m

Bohr’s model of the hydrogen atom provides insight into the behavior of matter at the microscopic level, but it is does not account for electron–electron interactions in atoms with more than one electron. It does introduce several important features of all models used to describe the distribution of electrons in an atom. These features include the following:

• The energies of electrons (energy levels) in an atom are quantized, described by quantum numbers : integer numbers having only specific allowed value and used to characterize the arrangement of electrons in an atom.
• An electron’s energy increases with increasing distance from the nucleus.
• The discrete energies (lines) in the spectra of the elements result from quantized electronic energies.

Of these features, the most important is the postulate of quantized energy levels for an electron in an atom. As a consequence, the model laid the foundation for the quantum mechanical model of the atom. Bohr won a Nobel Prize in Physics for his contributions to our understanding of the structure of atoms and how that is related to line spectra emissions.

## Key concepts and summary

Bohr incorporated Planck’s and Einstein’s quantization ideas into a model of the hydrogen atom that resolved the paradox of atom stability and discrete spectra. The Bohr model of the hydrogen atom explains the connection between the quantization of photons and the quantized emission from atoms. Bohr described the hydrogen atom in terms of an electron moving in a circular orbit about a nucleus. He postulated that the electron was restricted to certain orbits characterized by discrete energies. Transitions between these allowed orbits result in the absorption or emission of photons. When an electron moves from a higher-energy orbit to a more stable one, energy is emitted in the form of a photon. To move an electron from a stable orbit to a more excited one, a photon of energy must be absorbed. Using the Bohr model, we can calculate the energy of an electron and the radius of its orbit in any one-electron system.

What is pressure
Why does carbonic acid don't react with metals
Why does carbonic acid don't react with metal
Some metals will react depending on their Standard Electrode Potential. Carbonic acid is a very weak acid (i.e. a low hydrogen ion concentration) so the rate of reaction is very low.
Paul
sample of carbon-12 has a mass of 6.00g. How many atoms of carbon-12 are in the sample
a sample of carbon-12 has a mass of 6.00g. How many atoms of carbon-12 are in the sample
an object of weight 10N immersed in a liquid displaces a quantity of d liquid.if d liquid displaced weights 6N.determine d up thrust of the object
how human discover earth is not flat
We don't fall off. If set off in any direction in a straight line and keep going. You'll end up back where you started.
earth is spherical
Unique
Also, every other planet is spherical as that is the most energy efficient shape. gravity pulls equally on all areas. Sphere.
what is an ion
an atom that loses or gains an electron. Atoms normally have the same number of protons and electrons, therefore there is no charge as each + cancels out each -. When an atom loses an electron, it has more protons that electrons. Therefore the ion is called positive.
When an atom gains electrons it has more of them than protons. Therefore the ion is negative. You cannot change the number of protons as this results in a different element.
Gaining or losing electrons is based around the octet rule. 8 electrons in the outer shell is the most stable electron configuration (for the first three rows in the periodic table. After that it gets confusing so don't worry) So all atoms want to achieve this configuration.
Wat is chemical bonding
how to determine the number of atoms and the mass of zirconium, silicon, and oxygen found in 0.3384 mol of zircon4
what is a catalyst
A substance that speeds up the rate of a given reaction but does not react with any reactants
Brandon
something that speeds up a chemical reaction without being used up itself. It lowers the activation energy
something that speed up a chemical reaction without its self been used
Zainab
A catalyst is a substance that alters the rate of a reaction.. Meaning it can slow down a reaction or speeden it but it remains unchanged at the end of the reaction
Stellamaris
anything that speed up the rate of chemical reaction but it not being produced or consumed by the reaction
IBRAHIM
Faraday's first law of electrolysis state that...
the mass of a substance librated during electrolysis is directly proportional to the quantity of electricity passing through the electrolyte
Zainab
nice
Owolabi
greeaat
Abdul
another question
Owolabi
ys
Abdul
good
olanrewaju
gud one pls write it mathematically
Lekan
How can ionic bonds dissociate in aqueous solution
Because of the polarity of both ionic compounds and water the ionic compound will dissolve as "like dissolves like", and the molecule forms bonds with the water.
Claud
are all aqueous solutions water contained?
blossom
No, but a lot are.
Claud
it dissociate when d metal is combined wit oxygen
Lekan
I wanna understand more about isomers
Isomers are essentially the same molecules of one particular substance, except with different bonding points along the molecule. if you want a better example, look up xylene, p-xylene, and m-xylene. isomers are more for organic chemistry
Aaron
what is catenation
The property of carbon to form long chain with other atom!
Lareb
hydrocarbons can be classified as..1.Aliphatic compounds 2.cyclic compounds.under aliphatic compounds there are two types saturated hydrocarbons(alkanes) and unsaturated hydrocarbons(alkenes and alkynes).
thanks but i have also heard of aromatic hydrocarbons
emmanuel
so am kinda confused
emmanuel
how
Emmanuel
hydrocarbons are classified into 2 namely: aliphatic compound and aromatic compound
Mgbachi
aliphatic compound and aromatic compound
Mgbachi
what is bigonal relationship