Potential difference of a group of atoms

[HuaYongLi]

I encountered a question in my book:

a)An electron is trapped in a solid between a group of atoms where the potential is +2.8V
The de Broglie wavelength of this electron is 1.2nm. Calculate
i) its speed
ii) its kinetic energy
iii) the sum of its kinetic energy and its potential energy
b)i) Calculate the energy of a photon of wavelength 650nm
ii)State and explain whether or not the electron in part a) can escape from this group of atoms as a result of absorbing this photon

I can do the whole question via formulae "taught" to me and find that the resolved kinetic energy after the photon absorption will result in it escaping.

But I have some problems with the question itself, it says the electron is "trapped". I would have thought since it is trapped it was stationary.

Also I do not understand what is trying to get across when it mentions "potential", is this the potential that the electron needs to cross to escape?

I don't think I fully understand potential differences, would placing 2 opposite charges far from each other and close together result in the same potential difference and consequently the same KE? I always thought that placing 2 charges away from each other no matter the distance (Electromagnetic force has infinite range) would attract each other, closing the distance and also increasing the force.

I thought that momentum and KE are both conserved in a closed system. Say you had 2 particles of equal opposing momentums and you collided them both so they both stopped.
Particle 1 - 0.5kg - 1 m/s
Particle 2 - 1kg - 0.5m/s
But Particle 1 has a KE of 0.25J
and Particle 2 has a KE of (relatively) 0.125J
0.25-0.125=0.125J
If both particles are now stationary, where has the extra KE gone when KE is also meant to be conserved?

A lot of questions here, sorry.
Thanks

 

[JaWiB]

But I have some problems with the question itself, it says the electron is "trapped". I would have thought since it is trapped it was stationary.

Also I do not understand what is trying to get across when it mentions "potential", is this the potential that the electron needs to cross to escape?

"Trapped" means it's in some sort of potential well. Think of a ball rolling around in a bowl--it can be moving, but unless it has enough kinetic energy it can't get out of the bowl. In this case though the potential isn't gravitational but electric.

I don't think I fully understand potential differences, would placing 2 opposite charges far from each other and close together result in the same potential difference and consequently the same KE? I always thought that placing 2 charges away from each other no matter the distance (Electromagnetic force has infinite range) would attract each other, closing the distance and also increasing the force.

Two charges that are far apart have a greater potential than two (of the same magnitude) that are close together. I'm not exactly sure what your confusion is here.

I thought that momentum and KE are both conserved in a closed system. Say you had 2 particles of equal opposing momentums and you collided them both so they both stopped.
Particle 1 - 0.5kg - 1 m/s
Particle 2 - 1kg - 0.5m/s
But Particle 1 has a KE of 0.25J
and Particle 2 has a KE of (relatively) 0.125J
0.25-0.125=0.125J
If both particles are now stationary, where has the extra KE gone when KE is also meant to be conserved?

I'm not sure this corresponds to a physical situation. In real life, two masses can collide and stick together, but the energy probably goes into thermal motion of the molecules that make up the objects (or into surrounding air molecules), so the temperature goes up. If your two particles are electrons, for instance, then I think that they would have to be deflected and they couldn't stick together.