In the Bohr model of the hydrogen atom, the speed of the electron is approximately 2.1 × 106 m/s.
Find the central force acting on the electron as it revolves in a circular orbit of radius 4.51 × 10−11 m.
Answer in units of N
F=ma=mv²/R
To find the central force acting on the electron in the Bohr model of the hydrogen atom, we can use the centripetal force formula. The centripetal force is provided by the electrostatic force of attraction between the electron and the nucleus.
The formula for centripetal force is:
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.
We know the speed of the electron (v) is approximately 2.1 × 10^6 m/s and the radius of the orbit (r) is 4.51 × 10^-11 m.
The given mass of the electron is approximately 9.11 × 10^-31 kg.
Substituting the values into the formula, we get:
F = (9.11 × 10^-31 kg * (2.1 × 10^6 m/s)^2) / (4.51 × 10^-11 m)
Calculating this expression gives us the central force acting on the electron.
F = 9.11 × 10^-31 kg * (2.1 × 10^6 m/s)^2 / (4.51 × 10^-11 m)
= 42.3 N
Therefore, the central force acting on the electron in the circular orbit is approximately 42.3 Newtons (N).