# Conceptual Question: Energy of ions across a voltage difference

The following is a multiple choice question on a previous quiz I was given:

## Homework Statement

Ions of type A with a charge of +2e and a mass of 4 amu (atomic mass units) and ions of type B
with a charge of +3e and a mass of 20 amu are at rest on one side of a cell wall. Both pass
through the cell wall which has a voltage difference of 1.5 volts across it. When the ions leave
the cell wall

(a) they have the same energy.
(b) ions A have 1/5 the energy of ions B.
(c) ions A have 2/3 the energy of ions B.
(d) ions A have 5 times the energy of ions B.
(e) ions A have 10/3 the energy of ions B.

## Homework Equations

I have a feeling that I need to use F = ma somewhere, but I'm not sure how to relate the energy to the charge. Maybe W = F*d? I'm really lost and muddled.

## The Attempt at a Solution

Alright, this is just a basic concept question that I missed on a quiz awhile ago. I'm not sure what equation to use to relate energy, charge and mass. In fact, I'm starting to mix up my electric field equations with my energy equations and things are just getting plain messy. I have a feeling that I need to us F=ma and I know there has to be an equation relating force and energy, I'm just not sure where or how to find it.

Any hints or tips would be really helpful; thanks.

Kris

Andrew Mason
Homework Helper
The following is a multiple choice question on a previous quiz I was given:

## Homework Statement

Ions of type A with a charge of +2e and a mass of 4 amu (atomic mass units) and ions of type B
with a charge of +3e and a mass of 20 amu are at rest on one side of a cell wall. Both pass
through the cell wall which has a voltage difference of 1.5 volts across it. When the ions leave
the cell wall

(a) they have the same energy.
(b) ions A have 1/5 the energy of ions B.
(c) ions A have 2/3 the energy of ions B.
(d) ions A have 5 times the energy of ions B.
(e) ions A have 10/3 the energy of ions B.

## Homework Equations

I have a feeling that I need to use F = ma somewhere, but I'm not sure how to relate the energy to the charge. Maybe W = F*d? I'm really lost and muddled.

## The Attempt at a Solution

Alright, this is just a basic concept question that I missed on a quiz awhile ago. I'm not sure what equation to use to relate energy, charge and mass. In fact, I'm starting to mix up my electric field equations with my energy equations and things are just getting plain messy. I have a feeling that I need to us F=ma and I know there has to be an equation relating force and energy, I'm just not sure where or how to find it.

Any hints or tips would be really helpful; thanks.

Kris
The energy that the ions gain is a function of the electric charge (in Coulombs) and the potential difference (in units of energy/Coulomb), not mass. Mass has nothing more to do with the energy gained in an electrical field than charge has to do with the energy an object gains in a gravitational field.

That should make it pretty easy for you to answer.

AM

Wow, thank you. That made it embarrassingly easy. It'd be answer "c" then.

I suppose that's the effects of cramming.

Thanks, especially for the quick reply!