# Acceleration of an electron held at 1m from the nucleus of an Uranium atom.

• mxdrk
In summary, the problem states that an electron is held fixed at a distance of 1 m from the nucleus of a uranium atom with Z=92. The question is asking for the magnitude of the electron's initial acceleration when it is released. The solution involves using Coulomb's law to calculate the electrical force between the positively charged nucleus and the electron. The answer is 23,300 m/s^2.
mxdrk

## Homework Statement

An electron is held fixed at a distance of 1 m from the nucleus of a uranium atom (Z = 92). If the electron is then released, what is the magnitude of its initial acceleration?

## Homework Equations

I am not sure which kinematic equation that I should use.

## The Attempt at a Solution

This is the only problem on my physics final review that I do not know how to do. I know that the answer is 23,300 m/s^2, but I do not know how to get this answer. I would really love it if someone could explain how to solve this to me.

This is a dynamics problem, not a kinematics one. Hint: What force acts on the electron?

I was thinking the strong nuclear force, but I believe at 1m it is too far for that to have an effect. The only other thing I could think of would be gravity?

mxdrk said:
I was thinking the strong nuclear force, but I believe at 1m it is too far for that to have an effect. The only other thing I could think of would be gravity?
Neither of those forces would be significant. What other force acts?

The only other thing I could think of would be Coulomb's law. This is the only problem out of 100 that I just have no clue about. I keep rereading my notes but can't seem to find out what I'm missing on.

Thanks for the help though, I appreciate you trying to lead me to the answer.

mxdrk said:
The only other thing I could think of would be Coulomb's law.
That's the one.

The positively charged nucleus attracts the electron with an electrical force given by Coulomb's law. Figure out that force.

Thanks! Here, it was an incredibly easy problem.

## What is the formula for calculating the acceleration of an electron held at 1m from the nucleus of an Uranium atom?

The formula for calculating the acceleration of an electron at a given distance from the nucleus is a = (k * Q) / r^2, where k is the Coulomb constant, Q is the charge of the nucleus, and r is the distance between the electron and nucleus.

## How does the acceleration of an electron change as it gets closer to the nucleus of an Uranium atom?

The acceleration of an electron increases as it gets closer to the nucleus of an Uranium atom, due to the increasing strength of the electrostatic force between the two particles.

## What is the relationship between the acceleration of an electron and its distance from the nucleus of an Uranium atom?

The relationship between the acceleration of an electron and its distance from the nucleus of an Uranium atom is inversely proportional. This means that as the distance between the electron and nucleus decreases, the acceleration increases.

## How does the charge of the nucleus affect the acceleration of an electron held at 1m from the nucleus of an Uranium atom?

The charge of the nucleus directly affects the acceleration of an electron. As the charge of the nucleus increases, the acceleration of the electron also increases.

## Is the acceleration of an electron held at 1m from the nucleus of an Uranium atom constant?

No, the acceleration of an electron held at 1m from the nucleus of an Uranium atom is not constant. It constantly changes as the distance between the electron and nucleus changes due to the varying electrostatic force between them.

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