# Finding the wavelength

1. Aug 2, 2011

### Saitama

1. The problem statement, all variables and given/known data
H-atom is exposed to electromagnetic radiation of $\lambda$=1025.6 $\dot{A}$ and excited atom gives out induced radiations. What is the minimum wavelength of these induced radiation:
(a)102.6 nm
(b)12.09 nm
(c)121.6 nm
(d)810.8 nm

2. Relevant equations

3. The attempt at a solution

What does the question mean by "induced radiation"?

2. Aug 2, 2011

### PeterO

The Hydrogen atom may be excited by the radiation to change to an excited state. The atom then drops bag to its original state, giving off a photon. That is the induced radiation.

3. Aug 2, 2011

### Saitama

Thanks for explaining, but how should i start?

4. Aug 2, 2011

### PeterO

Suppose the atom was excited to the second level by these Photons, What wavelengths of induced radiation might you get? And what might that tell you?

it is 12:40 pm here I am off to bed.

5. Aug 2, 2011

### pmsrw3

The fundamental idea is that you never get more energy out than you put in.

6. Aug 2, 2011

### Saitama

I am taking hydrogen atom for example.
If i apply Rydberg formula, i get a wavelength of $\frac{4}{3R}$.

But i still don't understand what i have to do?

(Good night PeterO)

7. Aug 2, 2011

### I like Serena

Hi Pranav-Arora!

Fill in R?
What is the corresponding wavelength?
Is it more or less than the exposed wavelength?
That is, does this induced radiation contain more or less energy than the exposed energy?

8. Aug 2, 2011

### Saitama

I still don't get it.

9. Aug 2, 2011

### I like Serena

R is the Rydberg constant.
In e.g. wikipedia you can find its value.

What you get is the wavelength of induced radiation.
The shorter the wavelength the higher the energy.
Induced radiation will always have a wavelength longer than the wavelength of the exposed radiation (can't create energy out of nothing).

What is the value of R?
What do you get if you fill it in?
Is it bigger or smaller than the exposed radiation?

Once you have that we can continue.

10. Aug 2, 2011

### Saitama

Hi!!
I know what is "R".
$\frac{4}{3R}$, this value came because i assumed that electron jumped to the second level and came back. In the question, it's not specified that to which level electron jumps.

11. Aug 2, 2011

### I like Serena

No, it is not specified.
The electron could jump to the second level and back, or it could jump to the third level and back, or it could jump to the third level, fall back to the second level and fall back the the first level, etcetera.

Your job is to find the highest level it could jump to, deduce which possible radiations could come out, and decide which one fits the question.

12. Aug 2, 2011

### Saitama

13. Aug 2, 2011

### I like Serena

$$\infty$$

14. Aug 2, 2011

### PeterO

MORE IMPORTANT: HOW DOES THE ENERGY OF A WAVE COMPARE TO WAVELENGTH.

Does higher energy mean longer wavelength or does higher energy mean shorter wavelength?

15. Aug 2, 2011

### PeterO

Can it get there with this incoming radiation?

16. Aug 4, 2011

### Saitama

This question is getting off my mind.
Let's begin from starting.

PeterO, you said that "The Hydrogen atom may be excited by the radiation to change to an excited state. The atom then drops back to its original state, giving off a photon. That is the induced radiation."

Doesn't the atom absorbs a photon when it goes to the excited state?

17. Aug 4, 2011

### I like Serena

Yes, the atom absorbs a photon when it goes to the excited state.
This works out as an electron going to a higher energy level (there are only specific discrete energy levels).
After that the electron falls back to a lower energy level, giving off an induced photon.
The energy of the induced photon is equal to the difference in energy levels of the electron.

18. Aug 4, 2011

### I like Serena

No it can't.
To solve the problem the highest level must be calculated, based on the wavelength of the incoming radiation, and the wavelengths given by the Rydberg formula for the difference in energy levels that an electron can be in.

19. Aug 4, 2011

### Saitama

So how would it help in solving this problem?

20. Aug 4, 2011

### I like Serena

The rydberg formula gives you the wavelengths of the possible induced photons.
(Btw, the related energy of a photon of a wavelength lambda is E = h c / lambda.)
An induced photon can not have more energy than the photon that excited the atom.

Can you give me the wavelength belonging to an induced photon if the electron falls back from the second energy level to the first energy level (the ground state)?