# Wavelength with just enough energy

1. Apr 18, 2014

### Zondrina

1. The problem statement, all variables and given/known data

The work function for chromium is $7.0 \times 10^{-19} J$.

What is the wavelength of the light that has just enough energy to cause electrons to be emitted from chromium metal?

What is the work function of chromium, in kJ/mol?

2. Relevant equations

3. The attempt at a solution

I believe this question is missing some information? Here's what I have so far:

$E = K_e + W$
$\frac{hc}{\lambda} = K_e + W$
$\lambda = \frac{hc}{K_e + W}$

I can't exactly find the kinetic energy here I think.

The second question is easy, just convert the work function to kJ and take it per mol.

2. Apr 18, 2014

### BOYLANATOR

What does it tell you that it is just enough energy to cause an electron emitted?

3. Apr 18, 2014

### Zondrina

That is unfortunately the missing piece of information I believe.

4. Apr 18, 2014

### BOYLANATOR

Actually, you have enough information. Consider:

Case A) The photon has just enough energy to cause the electron to escape the atom.

Case B) The photon has much more energy than the minimum required to cause an electron to escape.

In both cases, 1 electron is emitted. What is the difference between the emitted electrons?

5. Apr 18, 2014

### Zondrina

Wait are you saying I need to consider when the kinetic energy is zero? So I could consider:

$E > W$
$\frac{hc}{\lambda} > W$
$\lambda < \frac{hc}{W}$

So when the wavelength is smaller than $\frac{hc}{W}$, the light will have just enough energy?

6. Apr 18, 2014

### BOYLANATOR

Well, when the wavelength is smaller than $\frac{hc}{λ}$ it has more than enough energy.

7. Apr 18, 2014

### Zondrina

Ah I understand now. So choosing $\lambda = \frac{hc}{W}$ is going to ensure there is just enough energy. Choosing it larger will create an excess of kinetic energy.

8. Apr 18, 2014

### BOYLANATOR

Yes you have it now. Just be careful on your wording: a smaller wavelength gives it an excess because smaller wavelength is bigger energy.

9. Apr 18, 2014

### Zondrina

Yes I meant choose it smaller from the inequality above, silly me.