[hoo boy]

I learned that electrons need to be hit by light of a certain energy to jump up to higher orbitals. My understanding was as such:

Ex: An electron needs 500J to jump up from n = 1 to n = 2 and an electron needs 750J to jump from n = 1 to n = 3.

I thought that if the light that hits has 500J, 501J or 749J then the electron will be able to make it to the n = 2 level. If it was 750J or higher then the electron would jump up to the n = 3 shell. [i.e. that jumping up to a shell requires a minimum energy and that if that is met (or higher) the electron will reach that shell].

But, my teacher today told us that absorption spectra are the same as emission spectra, which means that if the electron is hit by a 501J or 749J light it won't jump up to n = 2.

Can you guys clarify? If it doesn't jump up, what happens to it?

[Corribus]

The easy but not rigorous answer is that there is a resonance condition for transition of electron from one quantized orbit to another in response to an incoming photon . If the photon does not possess the right energy, it goes on its merry way - it's not absorbed and passes through.

I reality, the resonance condition is smudgy. Which is to say that as long as the photon energy is close to the resonance energy, there's a good probability that it will be absorbed. This is because of the uncertainty principle, which states puts a limit on the precision to which energy and time can be known simultaneously. Because transitions take a finite amount of time, there's also a finite wiggle room to their allowed energy values. This results in a finite linewidth to a spectroscopic transition, even one for an atom in a vacuum. We think of spectral lines from stars as "lines", but in fact they are very narrow bands. The width is defined by this smudginess.

Also, the resonance condition is a necessary but not sufficient criterion for absorption. There are a lot of other things that determine whether a photon is likely to be absorbed. So even if the photon has the right energy, it still may pass through unabsorbed. In Beer's Law the extinction coefficient (molar absorptivity) can be related via Avogadro's number to something called the absorption cross-section, which has a unit of area. It may be interpreted classically as a physical area through which a photon has to pass in order to be absorbed by the electron - kind of like a window if you will. The size of the area relates to the probability that a photon of a certain wavelength has of being absorbed by a single absorber (molecule, atom, whatever). The bigger the cross-section, the bigger the window, the higher probability of being absorbed. (The extinction coefficient, remember, has a unit of M^-1 cm^-1, or m²/Mol. So the molecular equivalent is m².)

[Enthalpy]

The example figures are unreasonable. Photons with 500J energy, or 3×10²¹eV, have not been detected up to now
https://en.wikipedia.org/wiki/Oh-My-God_particle
and no atom resonates at such an energy, its nucleus neither. Slash the figures by 10²¹, and you have common electronic transitions, in the order of 1eV.

Electronic transitions themselves have a finite duration hence energy selectivity, but often, the environment of the atom or molecule limits the time during which the transition can occur, and over this limited time, a photon energy a bit different from the perfect one is nearly as good. The approximate criterion is: over the absorption time, the phase of the photon rotates, the phase of the sum of both electron wavefunctions too, and the mismatch should not exceed one radian. One time limit results from the collisions between atoms or molecules, like 1ns in a usual gas on Earth and 1ps in a liquid, telling that no resonance of water can be observed in a microwave oven.

The other big widener of electronic transitions is the Doppler effect. At room temperature, molecules in a gas have a speed around 300m/s, or c/10⁶, so even if a photon is 10^-6 away from the perfect energy, some molecule will have the proper speed to absorb it.

[hoo boy]

The easy but not rigorous answer is that there is a resonance condition for transition of electron from one quantized orbit to another in response to an incoming photon . If the photon does not possess the right energy, it goes on its merry way - it's not absorbed and passes through.

I reality, the resonance condition is smudgy. Which is to say that as long as the photon energy is close to the resonance energy, there's a good probability that it will be absorbed. This is because of the uncertainty principle, which states puts a limit on the precision to which energy and time can be known simultaneously. Because transitions take a finite amount of time, there's also a finite wiggle room to their allowed energy values. This results in a finite linewidth to a spectroscopic transition, even one for an atom in a vacuum. We think of spectral lines from stars as "lines", but in fact they are very narrow bands. The width is defined by this smudginess.

Also, the resonance condition is a necessary but not sufficient criterion for absorption. There are a lot of other things that determine whether a photon is likely to be absorbed. So even if the photon has the right energy, it still may pass through unabsorbed. In Beer's Law the extinction coefficient (molar absorptivity) can be related via Avogadro's number to something called the absorption cross-section, which has a unit of area. It may be interpreted classically as a physical area through which a photon has to pass in order to be absorbed by the electron - kind of like a window if you will. The size of the area relates to the probability that a photon of a certain wavelength has of being absorbed by a single absorber (molecule, atom, whatever). The bigger the cross-section, the bigger the window, the higher probability of being absorbed. (The extinction coefficient, remember, has a unit of M^-1 cm^-1, or m²/Mol. So the molecular equivalent is m².)

Thank you so much!