Change in Electric potential, potential energy, and work problem.

In summary, the question asks for the work needed to remove the outermost electron from a lithium atom where the electrons and nucleus are all in a straight line. The answer is (kq^2/300)*10^12J, found by using the principle of superposition to calculate the electric potential at the outermost electron and then finding the difference in potential between the outer electron and the next energy level. However, the question is vague and it is unclear if the removal is to an infinite distance or to the next energy level.
  • #1
hongiddong
65
1

Homework Statement



Imagine a lithium atom where the two electrons in the first orbital are at exact opposite sides of the nucleus and the electron in the second orbital is in line with the other electrons so that the three electrons and the nucleus all lie on a straight line. How much work would you need to apply to remove the outer most electron if the atomic radius is 100picometer and the distance between the first and second orbital is 50picometer?

The answer is (kq^2/300)*10^12J.

Homework Equations



Based on the principle of superposition, I can find the electric potential at the outermost electron for lithium. (-kq)/50*10^-12+(3kq)/100*10^-12+(-kq)/150*10^-12 where k is the constant and a a is the type of charge.

The potential I find is then kq/300*10^-12.

To find work needed to move up, I need the electric potential "difference" from the outer electron to to the next level multiplied by a -q to get potential energy.(intuitively I know that potential energy will be positive and work will be negative; therefore the work applied must be positive.)

I don't know how the book just found this potential difference and ultimately the answer choice.

I have this feeling that the book left out information to the point that this problem is impossible to solve.
 
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  • #2
hongiddong said:
Based on the principle of superposition, I can find the electric potential at the outermost electron for lithium. (-kq)/50*10^-12+(3kq)/100*10^-12+(-kq)/150*10^-12 where k is the constant and a a is the type of charge.

The potential I find is then kq/300*10^-12.

That looks good.

To find work needed to move up, I need the electric potential "difference" from the outer electron to the next level multiplied by a -q to get potential energy.

My interpretation of the question is that you want to remove the outer electron all the way to infinite distance from the atom, rather than to the next energy level. But the question statement is not very clear.

(intuitively I know that potential energy will be positive and work will be negative; therefore the work applied must be positive.)

Be careful with the signs. Note that you are asked to find the work you would have to do to remove the electron (not the work done by the electric force).
 
  • #3
Dear Tsny,

The only way to find work is to know the change in electric potential, and the work applied would be the -of the work done by the electric field. I agree, this question is vague. If it were to move an infinite distance from the atom, how would I use that to get the right answer?
 

1. What is electric potential?

Electric potential is a measure of the potential energy that a charged particle possesses in an electric field. It is measured in volts (V) and is the amount of work needed to move a unit charge from one point to another in an electric field.

2. How does electric potential change in a circuit?

In a circuit, electric potential can change due to the presence of components such as batteries or resistors. Batteries add energy to the circuit, increasing the electric potential, while resistors decrease the electric potential by converting it into other forms of energy, such as heat.

3. What is the relationship between electric potential and potential energy?

Electric potential and potential energy are closely related. Electric potential is the amount of potential energy per unit charge, so an increase in electric potential results in an increase in potential energy. This means that a charged particle will have more potential energy when placed in a region with a higher electric potential.

4. Can you calculate work using electric potential?

Yes, work can be calculated using electric potential. The work done on a charged particle by an electric field is equal to the change in electric potential energy. This can be calculated using the equation W = qΔV, where q is the charge of the particle and ΔV is the change in electric potential.

5. How can I apply the concepts of electric potential, potential energy, and work in real-life situations?

The concepts of electric potential, potential energy, and work are commonly used in many real-life situations, such as in the design and operation of electrical circuits, the functioning of batteries and generators, and the behavior of charged particles in electric fields. These concepts are also important in understanding the principles behind technologies such as electrostatic precipitators and particle accelerators.

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