[Physics] No photoelectron is emitted from which of the following metals?


So there was this multiple choice question in an exercise in a bookI'm reading. I know that the forum is about discussions. But I want to know what the answer to the question is and why it is so.

From which of the following metals will photoelectrons not be emitted (under normal conditions)?

a. Cesium
b. Potassium
c. Aluminium
d. Sodium

Now, my confusions circle Aluminium and Potassium. Cesium has a work function that is sufficiently low to exhibit photoelectric effect. Aluminium's work function borders on the threshold at just over 4. But in standard conditions Cesium is a fluid. And without a rigid characteristic metal lattice, the photoelectric effect is not going to work, is it? A little help with this would be nice.

Best Answer

Your confusion is justified since the value of the work function depends on the configuration of the atoms in the material, and therefore can vary significantly.

The work function values can be found in this Wikipedia article. I also have the 1975/1976 edition of the Handbook of Chemistry and Physics which contains a table of work functions, and separately lists the thermionic work function and the photoelectric work function.

Here are the values lists in those sources (rounded to the nearest tenth):

Element      Wikipedia     CRC Handbook
Sodium          2.4          2.1-2.3
Potassium       2.3          2.0-2.3
Aluminum      4.1-4.3        3.0-4.4  
Cesium          2.1      1.9-2.0  4.1-5.6

So if you just go by the Wikipedia values, then clearly aluminum is the answer. But the CRC handbook paints a more ambiguous picture, since the work function for Cesium falls into two ranges, depending on the state of the Cesium. Unfortunately, the CRC handbook doesn't say what conditions are needed for the range 1.9-2.0.

So Sodium and Potassium are definitely not the answer, Cesium may or may not be the answer depending on what state it's in, and Aluminum always has a high work function. So Aluminum is your best choice for the answer.

Allow me to also point out that Sodium, Potassium, and Cesium are all in the leftmost column of the periodic table, and have a single valence electron. It's therefore reasonable to expect that valence electron will behave similarly for all three elements (the photoelectron is almost certainly the outermost electron). Aluminum, on the other hand, has three valence electrons, so it's reasonable to expect it to behave differently.