The Bohr model of the hydrogen atom consists of an electron travelling in a circular orbit of radius 5.29 x 10-11 m around a proton. The attraction between the two gives the electron the centripetal force required to stay in orbit. Calculate the:
a. Electric force between the two particles.
b. Speed of the electron.
c. Electric field the electron experiences.
d. Electric potential difference the electron experiences.
k =9•10^9 N•m²/C²,
e =1.6•10^-19 C.
r = 5.29•10^-11 m ,
m(electron) = m = 9.1•10^-31 kg
a.F =k•e²/r²,
m•v²/r = k•e²/r²,
b. v=sqrt(k•e²/m•r),
c. E =k•e/r²,
d.φ = - k•e/r,
Thanx elena for all the answers :-)
To calculate the values requested, we can utilize the principles of Newton's Law of Universal Gravitation and Coulomb's Law. Let's break down each calculation step by step:
a. Electric force between the two particles:
The electric force between the electron and proton can be calculated using Coulomb's Law:
Electric force (F) = (k * q1 * q2) / r^2
where k is the electrostatic constant (8.9875 x 10^9 N m^2/C^2), q1 and q2 are the charges of the electron and proton respectively, and r is the distance between them.
Since the electron has a charge of -1.6 x 10^-19 C and the proton has a charge of +1.6 x 10^-19 C, and the distance r is given as 5.29 x 10^-11 m, we can substitute these values into the formula:
F = (8.9875 x 10^9 N m^2/C^2) * (-1.6 x 10^-19 C) * (1.6 x 10^-19 C) / (5.29 x 10^-11 m)^2
By evaluating this expression, you will get the value for the electric force between the particles.
b. Speed of the electron:
The centripetal force required for the electron to stay in orbit is provided by the electric force between the electron and the proton. This force is given by:
Centripetal force = Electric force
The centripetal force can also be calculated using:
Centripetal force (Fc) = (m * v^2) / r
where m is the mass of the electron, v is its velocity or speed, and r is the orbit radius.
Equating the electric force and centripetal force, we get:
(m * v^2) / r = (8.9875 x 10^9 N m^2/C^2) * (-1.6 x 10^-19 C) * (1.6 x 10^-19 C) / (5.29 x 10^-11 m)^2
After substituting the values for charge, constants, and distance, you can solve for the speed of the electron.
c. Electric field the electron experiences:
The electric field experienced by the electron can be found using the formula:
Electric field (E) = F / q
where F is the electric force between the particles and q is the charge of the electron.
After calculating the electric force from part (a), you can substitute it into this formula along with the charge of the electron to determine the electric field.
d. Electric potential difference the electron experiences:
The electric potential difference, or voltage, is given by the formula:
Electric potential difference (V) = (k * q) / r
where k is the electrostatic constant, q is the charge of the proton, and r is the distance from the proton to the electron.
By substituting the appropriate values, you can calculate the electric potential difference experienced by the electron.
Remember, when performing calculations, it is essential to check the units and ensure they are consistent in order to obtain accurate results.