In the Bohr model of the hydrogen atom, the speed of the electron is approximately 2.17 x 10^6 m/s. find the central force acting on the electron as it revolves in a circular orbit of radius 5.42 x 10^-11m.
To find the central force acting on the electron in the circular orbit, you can use the centripetal force formula:
F = (m * v^2) / r
Where:
F is the central force
m is the mass of the electron
v is the speed of the electron
r is the radius of the orbit
Given:
v = 2.17 x 10^6 m/s
r = 5.42 x 10^-11 m
To calculate the central force, we need to know the mass of the electron. The mass of an electron is approximately 9.11 x 10^-31 kg.
Now, substitute the values into the formula:
F = (m * v^2) / r
F = (9.11 x 10^-31 kg) * (2.17 x 10^6 m/s)^2 / (5.42 x 10^-11 m)
Calculating this:
F = (9.11 x 10^-31 kg) * (4.7089 x 10^12 m^2/s^2) / (5.42 x 10^-11 m)
F = 4.1595673 x 10^-18 N
Therefore, the central force acting on the electron in the circular orbit is approximately 4.16 x 10^-18 N.
To find the central force acting on the electron in the Bohr model of the hydrogen atom, we can use the formula for centripetal force:
F = (m * v^2) / r
Where:
F is the centripetal force,
m is the mass of the electron,
v is the speed of the electron,
and r is the radius of the circular orbit.
In this case, the mass of the electron (m) is approximately 9.11 x 10^-31 kg, the speed of the electron (v) is approximately 2.17 x 10^6 m/s, and the radius of the orbit (r) is approximately 5.42 x 10^-11 m.
Plugging in these values into the formula, we get:
F = (9.11 x 10^-31 kg * (2.17 x 10^6 m/s)^2) / (5.42 x 10^-11 m)
Calculating this equation, we find:
F ≈ 3.66 x 10^-8 N
Therefore, the central force acting on the electron in the Bohr model of the hydrogen atom is approximately 3.66 x 10^-8 Newtons.