What Photon Energies Are Emitted When a Hypothetical Atom Absorbs 7-10 eV?

[ACraig21]

A gas of a hypothetical atom in ground state (-14eV) is irradiated with photons having a continuous range of energies between 7 and 10 electron-volts. Photons of which energies will be emitted from the gas?The energy levels look like this:
0-------------------(ionization state)
-1eV---------------
-3 eV--------------
-5 eV--------------

-10eV--------------
-14eV--------------Ground State

My Feeble Attempt:
I think that since it's emission, it can't be a continuous range of energies, so it is probably 1 eV, 5 eV, 7eV, and 10eV only, but I'm not sure at all. Any help would be greatly appreciated

 

[SammyS]

A gas of a hypothetical atom in ground state (-14eV) is irradiated with photons having a continuous range of energies between 7 and 10 electron-volts. Photons of which energies will be emitted from the gas?

The energy levels look like this:
0-------------------(ionization state)
-1eV---------------
-3 eV--------------
-5 eV--------------

-10eV--------------
-14eV--------------Ground State

My Feeble Attempt:
I think that since it's emission, it can't be a continuous range of energies, so it is probably 1 eV, 5 eV, 7eV, and 10eV only, but I'm not sure at all. Any help would be greatly appreciated

Hello ACraig21. Welcome to PF !

How did arrive at those results?

The method is more important than the answer.

 

[collinsmark]

Hello ACraig21,

Welcome to Physics Forums!

A gas of a hypothetical atom in ground state (-14eV) is irradiated with photons having a continuous range of energies between 7 and 10 electron-volts. Photons of which energies will be emitted from the gas?The energy levels look like this:
0-------------------(ionization state)
-1eV---------------
-3 eV--------------
-5 eV--------------

-10eV--------------
-14eV--------------Ground State

My Feeble Attempt:
I think that since it's emission, it can't be a continuous range of energies, so it is probably 1 eV, 5 eV, 7eV, and 10eV only, but I'm not sure at all. Any help would be greatly appreciated

Which energy states will electrons be "kicked" up to? The problem statement stipulated that the atoms are already in the ground state. So we start from there. Since the irradiating photons are only in the range of 7 to 10 eV, it means that the electrons will get "kicked" no more than 10 and no less than 7 eV above the ground state.

After that, start thinking about emissions as the electrons eventually fall back to the ground state. Keep in mind that on its way back, a given electron can fall directly back to the ground state, or the electron might fall to some intermediate state.

[Hint: the energy of the emitted photon is the difference between the electron's initial and final state. (And any of those states might be intermediate.) ]

 

[ACraig21]

That makes some sense, so the photons should have a range of emitted energies between 4 eV and 7 eV right? Unfortunately, the only answer choice in my packet to this problem that includes 4 eV also has 9 eV, so I'm still missing something.

 

[collinsmark]

That makes some sense, so the photons should have a range of emitted energies between 4 eV and 7 eV right? Unfortunately, the only answer choice in my packet to this problem that includes 4 eV also has 9 eV, so I'm still missing something.

As SammyS alluded to, the method of solving this problem is very important. I don't think you're using the right method.

There are two sets of photons that are important here. There are the photons that the atom absorbs and the photons that the atom emits.

Both sets will be of quantized energy levels.

Lets start by discussing the photons that are absorbed by the atom. The atom is only capable of absorbing certain wavelengths. The process by which this happens is that an electron will increase its energy state by the same amount as the photon energy. Since the problem statement stipulated that all atoms start their electrons in their ground state, it greatly narrows down the energy levels that can be absorbed (in this case). If an atom doesn't absorb a photon, the photon will pass right through the gas. In other words, the gas will be transparent to light at these frequencies (i.e. these wavelengths). That's why if you shine white light through a cold gas, the resulting spectrum shows dark, narrow "absorption lines" in an otherwise smooth spectrum. These lines correspond to the wavelengths of light that were absorbed.

When an atom emits a photon, the process is an electron moving from a higher energy state to a lower one (lower energy states are closer to the ground state). This can happen by an electron falling between adjacent energy states, or the electron could skip an energy state or two. The electron can even fall all the way down to the ground state. This is why when you look at the spectrum of a hot gas, all you see is bright, very narrow "emission lines" and nothing in between.

In both cases, absorption and emission, the energy level of the photons involved is the difference between the energy levels of the electron. This is important. The energy level of the photon is not the absolute energy level of the electron (in this case the absolute levels can be -14, -10, -5, -3 and -1 eV). Instead, it involves the difference between various combinations of absolute energy levels [such as perhaps -5 - (-10), or maybe -3 - (-14)].

The first step in solving this problem is to determine the possible absolute energy levels that an electron, starting in its ground state, can get "kicked" up to, when the irradiated photons (i.e. the set of photons that might be absorbed by the atom) are limited between 7 and 10 eV.

Once you have the possible (absolute) energy levels that the electron can get "kicked" up to, you can start looking at the possible differences between absolute energy levels that the electron might transition as it heads back down to the ground state.