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 the Bohr model of the hydrogen atom, we can use the centripetal force equation.
The centripetal force is given by the equation:
F = (m * v^2) / r
Where:
F is the centripetal force,
m is the mass of the electron,
v is the velocity of the electron,
r is the distance from the center of the orbit to the electron.
In this case:
m = mass of the electron = 9.11 x 10^-31 kg (standard value),
v = velocity of the electron = 1.97 x 10^6 m/s (given),
r = radius of the circular orbit = 4.72 x 10^-11 m (given).
Substituting the values into the equation, we have:
F = (9.11 x 10^-31 kg * (1.97 x 10^6 m/s)^2) / (4.72 x 10^-11 m)
Calculating this expression will give us the central force acting on the electron.
F = (9.11 x 10^-31 kg * 3.88 x 10^12 m^2/s^2) / (4.72 x 10^-11 m)
= 3.77 x 10^-8 N
Therefore, the central force acting on the electron in the Bohr model of the hydrogen atom is approximately 3.77 x 10^-8 N.
To find the central force acting on the electron, we can use the centripetal force formula:
F = (m * v^2) / r
Where:
F is the central force acting on the electron
m is the mass of the electron
v is the speed of the electron
r is the radius of the circular orbit
The mass of an electron is approximately 9.11 × 10^-31 kg.
Let's substitute the given values into the formula:
m = 9.11 × 10^-31 kg
v = 1.97 × 10^6 m/s
r = 4.72 × 10^-11 m
F = (9.11 × 10^-31 kg * (1.97 × 10^6 m/s)^2) / (4.72 × 10^-11 m)
Now, let's calculate the central force:
F ≈ (9.11 × 10^-31 kg * 3.88 × 10^12 m^2/s^2) / (4.72 × 10^-11 m)
F ≈ 3.778 × 10^-19 N
Therefore, the central force acting on the electron in the circular orbit of radius 4.72 × 10^-11 m is approximately 3.778 × 10^-19 N.