In the Bohr model of the hydrogen atom,
the speed of the electron is approximately
1.97 × 106 m/s.
Find the central force acting on the electron
as it revolves in a circular orbit of radius
4.72 × 10−11 m.
Answer in units of N.
To find the central force acting on the electron in a circular orbit in the Bohr model, we can use the centripetal force formula.
The centripetal force acting on an object moving in a circular path is given by the formula:
F = (m * v^2) / r
Where:
F is the force
m is the mass of the object
v is the velocity of the object
r is the radius of the circular path
In the case of the hydrogen atom, the electron is a point particle with a mass of about 9.11 x 10^-31 kg (approximate value).
The given velocity is 1.97 x 10^6 m/s, and the radius is 4.72 x 10^-11 m.
Substituting the values into the formula:
F = (9.11 x 10^-31 kg) * (1.97 x 10^6 m/s)^2 / (4.72 x 10^-11 m)
Now let's calculate the force:
F = (9.11 x 10^-31 kg) * (3.88 x 10^12 m^2/s^2) / (4.72 x 10^-11 m)
F = (9.11 x 3.88) * (10^-31 x 10^12) / (4.72 x 10^-11) kg * m^2/s^2
F = 35.3848 x 10^(-19-31+12+11) N
F = 35.3848 x 10^-27 N
F ≈ 3.538 x 10^-26 N
Therefore, the central force acting on the electron in the Bohr model of the hydrogen atom is approximately 3.538 x 10^-26 N.