• Miss1nik2
In summary, the problem involves finding the magnitude of an electron's centripetal acceleration in an orbit with a radius of 3.09 x 10-11 m around a nucleus containing two protons. Using Coulomb's law and the given mass of the electron, the calculated acceleration is 5.29 x 10 ^ 23, which is incorrect. Further assistance is needed to determine the correct answer.
Miss1nik2

Multiple-Concept Example 3 provides some pertinent background for this problem. Suppose a single electron orbits about a nucleus containing two protons (+2e), as would be the case for a helium atom from which one of the naturally occurring electrons is removed. The radius of the orbit is 3.09 x 10-11 m. Determine the magnitude of the electron's centripetal acceleration.

Multiple-Concept Example 3 tells you that the electron mass is 9.11 x 10 ^ -31 kg.

I know what I have to do...

First, use Coulomb's law to find the Force. Then, divide by mass to find the acceleration. But the answer I am getting is HUGE.

This is what I found...

F= 4.82 x 10 ^ 7

Then, a= 5.29 x 10 ^ 23.

Hi Miss1nik2!
Miss1nik2 said:
… the electron mass is 9.11 x 10 ^ -31 kg.

F= 4.82 x 10 ^ 7

Then, a= 5.29 x 10 ^ 23.

erm … you have 10 ^ 23 x 10 ^ -30 = 10 ^ 7

First of all, great job on using Coulomb's law to find the force between the electron and the nucleus! However, there seems to be a mistake in your calculation for the acceleration. Remember, acceleration is equal to force divided by mass (a = F/m). In this case, the mass of the electron is 9.11 x 10^-31 kg, so your calculation for acceleration should be:

a = (4.82 x 10^7 N) / (9.11 x 10^-31 kg)

This gives us a much more reasonable answer of 5.29 x 10^37 m/s^2. It's important to always check your units when doing calculations to make sure they are consistent. In this case, the units for force (N) and mass (kg) cancel out to give us the correct unit for acceleration (m/s^2). Keep up the good work!

## 1. What is an electron's acceleration?

An electron's acceleration refers to the rate at which its velocity changes over time. It is a measure of how quickly the electron's speed and/or direction is changing.

## 2. How is an electron's acceleration calculated?

An electron's acceleration can be calculated using the formula: a = F/m, where a is acceleration, F is the net force acting on the electron, and m is the electron's mass.

## 3. What factors affect an electron's acceleration?

An electron's acceleration is affected by several factors, including the magnitude and direction of the net force acting on it, its mass, and the medium through which it is moving.

## 4. Why is an electron's acceleration important in science?

An electron's acceleration is important in science because it helps us understand the behavior of charged particles and their interactions with electromagnetic fields. It also plays a crucial role in various fields such as electronics, quantum mechanics, and astrophysics.

## 5. Can an electron's acceleration be negative?

Yes, an electron's acceleration can be negative if the net force acting on it is in the opposite direction of its initial velocity. This means that the electron will decelerate or slow down over time.

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