Sodium has a work function of 2.28 eV. Let's say, I introduce a very strong external electric field, which is applying a force on the electrons outwards, thus giving them electrical potential energy of 1.5 eV each. What is the work function of the metal surface in such a case?
Sodium has a work function of 2.28 eV. Let's say, I introduce a very strong external electric field, which is applying a force on the electrons outwards, thus giving them electrical potential energy of 1.5 eV each. What is the work function of the metal surface in such a case?
The correct option is C 2.28 eV
The work function is a characteristic of the metal surface - meaning, it does not depend on external factors, like temperature, external electric fields, etc. But in this example, since the electric field is already providing some energy to the electrons, won't the minimum energy needed to come out of the surface decrease now? Yes, true. Then where are we going wrong? Consider the following analogy.
I am really late for class and I am not even within the school. So I decide to climb the boundary wall closest to my class and make a run
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To my disappointment, I find the wall to be 3 meters tall, while I stand at 1.5 meters only, and weigh 50 kgs. Since my potential energy on top of the wall would be approximately 50×10×3J=1500 J(simple application of P.E = mgh), I would require 1500 J to get on top. I decide to pile a few bricks to a height of 1 meter and stand on top of the pile. Since I'm closer to the top, I will require only (50×10×2) J = 1000 J of energy to make it. Sure, it's easier for me to make the jump now, but - has the height of the wall changed because of the pile of bricks? NO. The wall is still 3 meters high. The pile of bricks is merely an aid (I still had to spend 500 J to get on top of the pile of bricks).
The work function is defined as the minimum energy an electron requires to overcome the binding potential in the absence of external help, like energy from a light source, external electric fields, thermal energy, etc. This is a characteristic feature of the metal surface and does not change, just like the 1500 J of energy required to climb the entire height of the wall in our analogy.
2.28 eV
The work function is a characteristic of the metal surface - meaning, it does not depend on external factors, like temperature, external electric fields, etc. But in this example, since the electric field is already providing some energy to the electrons, won't the minimum energy needed to come out of the surface decrease now? Yes, true. Then where are we going wrong? Consider the following analogy.
I am really late for class and I am not even within the school. So I decide to climb the boundary wall closest to my class and make a run.
To my disappointment, I find the wall to be 3 meters tall, while I stand at 1.5 meters only, and weigh 50 kgs. Since my potential energy on top of the wall would be approximately 50×10×3J=1500 J(simple application of P.E = mgh), I would require 1500 J to get on top. I decide to pile a few bricks to a height of 1 meter and stand on top of the pile. Since I'm closer to the top, I will require only (50×10×2) J = 1000 J of energy to make it. Sure, it's easier for me to make the jump now, but - has the height of the wall changed because of the pile of bricks? NO. The wall is still 3 meters high. The pile of bricks is merely an aid (I still had to spend 500 J to get on top of the pile of bricks).
The work function is defined as the minimum energy an electron requires to overcome the binding potential in the absence of external help, like energy from a light source, external electric fields, thermal energy, etc. This is a characteristic feature of the metal surface and does not change, just like the 1500 J of energy required to climb the entire height of the wall in our analogy.
