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 occuring 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 Im getting is HUGE.
This is what I found....
F= 6.94 x 10 ^ -4.
Then, a= 7.62 x 10 ^26.
That is the wrong answer. Please help!!
see above.
To determine the magnitude of the electron's centripetal acceleration, we need to consider the electrostatic force acting between the electron and the nucleus.
First, let's calculate the electrostatic force using Coulomb's law. Coulomb's law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The charge of an electron is -1.6 x 10^-19 coulombs. The charge of a proton is +1.6 x 10^-19 coulombs. However, in this case, we have two protons in the nucleus, so the total charge of the nucleus is +3.2 x 10^-19 coulombs.
The distance between the electron and the nucleus is given as the radius of the orbit, which is 3.09 x 10^-11 m.
Using Coulomb's law, the electrostatic force (F) can be calculated as:
F = k * (|q1| * |q2|) / r^2
Where:
k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2)
q1 and q2 are the charges of the two objects
r is the distance between them
So, plugging in the values:
F = (8.99 x 10^9 N m^2/C^2) * (1.6 x 10^-19 C) * (3.2 x 10^-19 C) / (3.09 x 10^-11 m)^2
Calculating this expression, we find:
F ≈ 6.94 x 10^-4 N
Now, to find the magnitude of the electron's centripetal acceleration, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass:
a = F / m
The mass of the electron is given as 9.11 x 10^-31 kg.
Plugging in the values:
a = (6.94 x 10^-4 N) / (9.11 x 10^-31 kg)
Calculating this expression, we find:
a ≈ 7.62 x 10^26 m/s^2
It seems that you have correctly calculated the force, but made an error when dividing by the mass to find the acceleration. You should get a much smaller value.
Please recheck your calculations, and ensure that you have used the correct values for the charges, distances, and constants.