Question

Question #3abb5

Answer 1

I'd go with (d) Cannot tell.

Explanation:

The idea here is that an incoming photon's capacity to eject an electron from the surface of a metal depends on its frequency, as well as on the work function of the metal.

This is essentially what the Photoelectric Effect tells you--an incoming photon can eject an electron from the surface of a metal if its energy exceeds the work function of the metal.

`color(blue)(ul(color(black)("K"_ "E" = E_"photon" - W)))`

Here

• `"K"_"E"` is the kinetic energy of the ejected electron
• `E_"photon"` is the energy of the photon
• `W` is the work function of the metal

In order for a photon to be able to eject an electron from the surface of the metal, it must have

`E_"photon" >= W`

As you know, the energy of a photon is directly proportional to its frequency, i.e. the higher the frequency of the photon, the more energetic it will be.

So if you know that a photon of yellow light frequency cannot eject an electron from this unknown metal, you can say for certain that a more energetic photon, i.e. a photon of higher energy, is needed here.

As you can see, red light photons have a lower frequency than yellow light photons, so right from the start, you can say for sure that a red light photon will not be able to eject an electron from the surface of the metal.

On the other hand, green and blue light photons have higher frequencies than yellow light photons, so in theory, they could both eject electrons from the surface of this metal.

In order of increasing frequency, and implicitly, of increasing energy, you have photons of

`color(red)("red light") < color(gold)("yellow light") < color(green)("green light") < color(blue)("blue light")`

However, you don't have any information about the work function of the metal, i.e. how much energy is needed in order to remove an electron from the surface of the metal.

This means that the only valid answer that you can give here is (d) Cannot tell.

Photons of green and blue light could eject electrons from the surface of this metal, but you just can't say for sure if any would actually do it without knowing the work function of the metal.

`color(white)(a)`
SIDE NOTE If this is a multiple-choice question, then you can say that the answers are (b) Green and (c) Blue.