Wavelength with just enough energy

[STEMucator]

Homework Statement

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?

Homework Equations

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.

 

[BOYLANATOR]

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

 

[STEMucator]

That is unfortunately the missing piece of information I believe.

 

[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?

 

[STEMucator]

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?

 

[BOYLANATOR]

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

 

[STEMucator]

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

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.

 

[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.

 

[STEMucator]

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

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

Thank you for your help.