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# Possible frequencies of an electron watch

1. Hi
Could someone kindly clarify the following?

1. The problem statement, all variables and given/known data
In its ground state the atom absorbs 2.3 × 10?19J of energy from a collision with an electron.
(i) Calculate all the possible frequencies of radiation that the atom may subsequently emit.

2. Relevant equations
E=hf

3. The attempt at a solution
Using h as the planck constant and E being given , I obtained a frequency of 3.5 x 10^14 Hz.

But how do I determine the possible frequencies?
Highly appreciate any suggestions.
2. It depends what atom it is, and what the electron energy levels are.
As you haven't given this information it's impossible to say exactly.
The excited electron can fall to lower energy states and emit a photon E=hf where E is the energy difference between two energy levels and f the frequency.
3. In physics certain quantities are quantized and discrete, such as charge, and energy levels of an atom. Now what does this mean?

When a certain quantity is quantized or discrete, it means that it can only take upon certain values and nowhere in between.

Charge
We all know that charge will always be a multiple of elementary charge , meaning charges appear in the form of as integer multiples of .

Energy Levels in an atom
When describing the atom, some simply refer to the energy levels of the electron as the energy levels of the whole atom. Now let's try to prove that the energy levels in an atom are discrete.

Let's consider an electron trapped within a 1 dimensional potential well (for simplicity) as shown below.

Let's deduce some things:

1)The sides of the well are impossible areas, since the potential is infinitely high for the electron to exist there.

Following point 1, hence

2)The wavelengths of the electron must be confined to the well, and the possible energy states of the atom are:

But this only gives us the wavelength, and tells us nothing about the energy levels! Now we relate wavelength to energy:

(How did I get this? Try using E = 0.5mv^2)

Combining the 3 equations, you get the energy levels as:

Now what does this say about the energy levels of an electron? They are discrete as

Energy Levels of the Hydrogen atom
The energy levels of the hydrogen atom is derived using the Bohr Model, the explanation above simply shows that energy levels in atoms are quantized. http://en.wikipedia.org/wiki/Bohr_model

Let's use the case of the hydrogen atom:

What stonebridge meant: and varies from atom to atom

Key Points
1)When an electron collides with an atom; passing its energy, the atom gets energized.

2)When the atom relaxes, it releases its energy in the form of electromagnetic radiation (light) where the energy of the light is , where is the difference between any 2 energy levels

3)The emitting of light can take place between any 2 energy levels as long as the difference does not exceed the absorbed energy

Referring to the energy levels of the hydrogen atom (Refer to picture above)
Possible transition states are:

n = 4 to n = 3
Difference in energy = 0.661 eV

n = 5 to n = 3
Difference in energy = 0.967 eV

so on and so forth...

I hope this helps! (Wow what a long post...)
4. (Original post by BrilliantMinds)
...
Except an atom isn't an infinite well. You need to solve the TISE in spherical coordinates to get its energy levels. However the energy levels will depend on the type of atom and also the level of detail required ( ie whether you look at fine structure etc.)
5. (Original post by suneilr)
Except an atom isn't an infinite well. You need to solve the TISE in spherical coordinates to get its energy levels. However the energy levels will depend on the type of atom and also the level of detail required ( ie whether you look at fine structure etc.)
Yes, the electron spends most of its time within radius
6. First we should know what state electron is in. ( Can take help of heizenberg uncertinity principle). If the electron is moving to higher energy state or lower energy state.
If electron is going to lower energy state, it will emit a photon and that can be taken from E=hf.

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