Need help on how to find distance between electron and proton

[ken19]

1. According to the "Solar model" of a single ionized Helium atom has one electron revolving in a circular orbit around a stationary nucleus made of two protons and two newtrons. The diameter of this atom is .95*10^-10m. Use Coulomb's law and calculate the speed of the electron (m/s) in its orbit.

2. Homework Equations
Fe=K*q1*q2/d2 where k=8.99*10^9 Nm^2/s^2.
v=d/t

3. The Attempt at a Solution .
How do I go about solving this question when either of distance or time is given? Any help is appreciated.

 

[jackqpublic]

consider the protons as in the center of the atom.
the definition of atomic radius is the distance from the center of the atom to its farther electron.
so use the definition of centripetal force and you will get the velocity of the electron.
[;F=\frac{mv^2}{R};]
and [;F=\frac{K.Q_1.Q_2}{R^2};]

 

[tomcue]

Firstly, to find the distance between the electron and proton, we can use the given diameter of the atom (.95*10^-10m) and divide it by 2 to get the radius of the orbit. This would give us a radius of .475*10^-10m.

Next, we can use Coulomb's law to calculate the force between the electron and proton. We know that the force is equal to the product of the two charges (q1 and q2) divided by the square of the distance between them. In this case, q1 and q2 represent the charges of the electron and proton, respectively.

Since the atom is single ionized, the charge of the electron would be -1.6*10^-19C and the charge of the proton would be +1.6*10^-19C. Plugging in these values and the given distance (radius) into Coulomb's law equation, we can solve for the force (Fe).

Once we have the force, we can use the formula v=d/t to find the speed of the electron in its orbit. The distance in this case would be the circumference of the orbit (2πr) and the time would be the time it takes for the electron to complete one orbit (period).

To find the period, we can use the formula T=2π√(m*r^3/Fe), where m is the mass of the electron (9.11*10^-31kg) and r is the radius of the orbit. Once we have the period, we can plug it into the velocity formula to find the speed of the electron in its orbit.

I hope this helps in solving the problem. Let me know if you have any further questions.

 

[nlightner]

To find the distance between an electron and a proton, we can use Coulomb's law which states that the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In this case, we can use the distance given in the problem (.95*10^-10m) to calculate the force between the electron and proton.

Fe = K*q1*q2/d^2

Where:
Fe = electrostatic force
K = Coulomb's constant (8.99*10^9 Nm^2/C^2)
q1 and q2 = charges of the electron and proton respectively
d = distance between the electron and proton

Once we have calculated the force, we can use the centripetal force equation to find the speed of the electron in its orbit. This equation relates the speed of an object in circular motion to the radius of its orbit and the force acting on it.

Fc = mv^2/r

Where:
Fc = centripetal force
m = mass of the electron
v = speed of the electron
r = radius of the electron's orbit

Since we know the force (Fe) and the radius (d/2), we can rearrange the equation to solve for the speed (v).

v = √(Fc*r/m)

Substituting the values of Fc, r, and m, we get:

v = √(K*q1*q2/d^2 * d/2/m)

Simplifying, we get:

v = √(K*q1*q2/2m)

Now, we can plug in the values for the charges and the mass of the electron to calculate the speed. The final answer will be in meters per second (m/s).

I hope this helps! Let me know if you have any further questions.