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# Emission spectrum of hydrogen

The Balmer Rydberg equation explains the line spectrum of hydrogen. A line spectrum is a series of lines that represent the different energy levels of the an atom. In this video, we'll use the Balmer-Rydberg equation to solve for photon energy for n=3 to 2 transition. Created by Jay.

## Want to join the conversation?

• In a hydrogen atom, why would an electron fall back to any energy level other than the n=1, since there are no other electrons stopping it from falling there?
• The electron can only have specific states, nothing in between. By releasing a photon of a particular amount of energy, an electron can drop into one of the lower energy levels. If it happens to drop to an intermediate level, not n=1, the it is still in an excited state (albeit a lower excited state than it previously had). It will, if conditions allow, eventually drop back to n=1.

So, it is not a matter of the electron not returning to n=1, it is just that it might do so in a number of steps instead of all at once.
• So if an electron went from n=1 to n=2, no light would be emitted because it is absorbing light, not emitting light correct?
• yes but within short interval of time it would jump back and emit light
• what is meant by the statement "energy is quantized"?
• It means that you can't have any amount of energy you want. It has to be in multiples of some constant.

For an analogy, consider currency, there is a fixed smallest unit like 1 paisa or 1 cent and all other currency notes/coins are a multiple of that fixed unit.
• Just as an observation, it seems that the bigger the energy level drop that the electron makes (nj to n=2), the higher the energy of the wave that is emitted by the electron.
ex:
n3 to n2 : red
n4 to n2 : cyan
etc

But, the drop from n2 to n1 creates a wave with higher energy than n6 to n2 (122nm vs 410nm). Why is that ? is the energy difference between n2 and n1 really bigger than n6 to n2 ? or am i makinga big mistake ? haha

Thanks a lot !
• As the number of energy levels increases, the difference of energy between two consecutive energy levels decreases. See this,
Number of orbits-----Energy of orbits
n=1 -13.6 eV
n=2 -3.4 eV
n=3 -1.51 eV
n=4 -0.85 eV
n=5 -0.544 eV
n=6 -0.3778 eV
See how the difference of energy decreases. That is why, more energy is released when there is a transition from n2 to n1 rather than from n6 to n2.
Hope that helps.
• What is the relation between [(the difference between emission and absorption spectra) and (the difference between continuous and line/atomic spectra)]?
• Line spectra are produced when isolated atoms (e.g. in outer space or in high-vacuum tubes) emit or absorb only certain frequencies of energy (photons). Continuous spectra (absorption or emission) are produced when (1) energy levels are not quantized, but continuous, or (2) when zillions of energy levels are so close they are essentially continuous. The first occurs, for example, in plasmas like the Sun, where the temperatures are so high that the electrons are free to travel in straight lines until they encounter other electrons or positive ions. During these collisions, the electrons can gain or lose any amount of energy (within limits dictated by the temperature), so the spectrum is continuous (all frequencies or wavelengths of light are emitted or absorbed). The second case occurs in condensed states (solids and liquids), where the electrons are influenced by many, many electrons and nuclei in nearby atoms, and not just the closest ones. Because the electric force decreases as the square of the distance, it becomes weaker the farther apart the electric charged particles are, but there are many such particles, with the result that there are zillions of energy levels very close together, and transitions between all possible levels give rise to continuous spectra. Because solids and liquids have finite boiling points, the spectra of only a few (e.g. metals like tungsten, or oxides like cerium oxide in lantern mantles) include visible radiation. However, all solids and liquids at room temperature emit and absorb long-wavelength radiation in the infrared (IR) range of the electromagnetic spectrum, and the spectra are continuous, described accurately by the formula for the Planck black body spectrum. Infrared photons are invisible to the human eye, but can be felt as "heat rays" emitted from a hot solid surface like a cooling stove element (a red-hot stove or oven element gives off a small amount of visible light, red, but most of the energy emitted is in the infrared range). Hope this helps.
• My textbook says that there are 2 rydberg constant 2.18 x 10^-18 and 109,677
my teacher says that rydberg found 2 constants 'probably'
• They are related constants.
The Rydberg constant is:
R∞ = 109737 cm⁻¹ (though it is more often expressed in m⁻¹)

The number you quoted is the Rydberg constant for hydrogen, which is derived from the standard Rydberg constant and more than a few books get a little sloppy about and just call the "Rydberg constant". Its symbol is RH (the H is a subscript).
RH = R∞ [ MH / (me+MH) = 109677.58 cm⁻¹
Where,
MH (H is a subscript) is the mass of a proton
me (e is a subscript) is the mass of an electron

If you multiply R∞ by hc, then you get the Rydberg unit of energy, Ry, which equals 2.17987×10⁻¹⁸ J

Thus, Ry is derived from RH.
So, one of your numbers was RH and the other was Ry.

NOTE: I rounded off R∞, it is known to a lot of digits.
• Do all elements have line spectrums or can elements also have continuous spectrums?
• Atoms in the gas phase (e.g. in outer space or in high vacuum) have line spectra. However, atoms in condensed phases (solids or liquids) can have essentially continuous spectra. For example, the tungsten filaments in incandescent light bulbs give off all colours of the visible spectrum (although most of the electrical energy ends up emitted as infrared (IR) photons, explaining why tungsten filament light bulbs are only 5-10% energy efficient). The explanation comes from the band theory of the solid state: in metallic solids, the electronic energy levels of all the valence electrons form bands of zillions of energy levels packed really closely together, with the electrons essentially free to move from one to any other. All the possible transitions involve all possible frequencies, so the spectrum emitted is continuous. The band theory also explains electronic properties of semiconductors used in all popular electronics nowadays, so it is not BS.
• At , what is a Balmer Rydberg equation?
• The Balmer-Rydberg equation or, more simply, the Rydberg equation is the equation used in the video.
1/λ = R(1/i² -1/j²)
It is usually written as
1/λ = R(1/n₁² -1/n₂²), where n₁ < n₂.
For the Balmer series of lines ( the visible lines in the hydrogen spectrum), n₁ = 2.
So the Rydberg formula for the Balmer series of lines is
1/λ = R(1/4 - 1/n₂²).
• At -, Jay calls it a continuous spectrum. But, we know that the sun's light is created due to the emission spectra of different elements, mainly H, some He and even Lesser Li, along with trace amounts of Ca, Mg and a few others. While the sun's spectrum (so to call it) is continuous, Jay says at that H's spectrum would not be continuous, it'd be a line spectrum (as he says at ). I've also heard it being called a discrete spectrum. Why is it that though the same element creates the spectrum, one is continuous while the other isn't? Is it because the spectrum is made in different conditions (heat in case of the sun, while electricity in case of a spectrometer)? I don't see why that should happen, since energy is energy in whichever manner it is supplied, and because there is no way an electron would respond differently though it belonged to the nucleus of the same element. Please help. Thanks a lot.
• The discrete spectrum emitted by a H atom is a result of the energy levels within the atom, which arise from the way the electron interacts with the proton. To view the spectrum we need hydrogen in its gaseous form, so that the individual atoms are floating around, not interacting too much with one another.

The sun is not just a big ball of H atoms loosely floating around. For one thing, the temperature is very high, so the atoms are ionized. In other words, you have a lot of H nuclei (ie protons) and a lot of electrons, and they aren't bound together to make a nice simple H atom. Also, you have enormous pressure, which forces all of the atoms to interact with one another in a way that they don't when they are in low-pressure gas form. The interactions between the particles create a different, much larger set of energy levels that permit a continuous rather than discrete spectrum. The sun radiates like a so-called "black body" with temperature around 5700K.

When astronomers study distant stars they actually look at ABSORPTION spectra rather than emission spectra. The absorption spectrum is what's left after the white light passes through the outer layers of the star, where the pressure is lower and the protons can join with the electrons to make complete H atoms. The absorption spectrum is like the negative of the emission spectrum, it has dark lines where the emission spectrum has light. We identify the H in the star by seeing its characteristic absorption spectrum.