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 formula:
F = (m * v^2) / r
where F is the force, m is the mass of the electron, v is the speed of the electron, and r is the radius of the circular orbit.
Given:
v = 1.97 × 10^6 m/s (speed of the electron)
r = 4.72 × 10^-11 m (radius of the orbit)
The mass of the electron, m, is a known constant: 9.11 × 10^-31 kg.
Now we can plug in the values into the formula and solve for F:
F = (m * v^2) / r
F = (9.11 × 10^-31 kg) * (1.97 × 10^6 m/s)^2 / (4.72 × 10^-11 m)
Calculating these values, we get:
F = (9.11 × 10^-31 kg) * (3.89 × 10^12 m^2/s^2) / (4.72 × 10^-11 m)
F = (35.49 × 10^-19 kg * m^2/s^2) / (4.72 × 10^-11 m)
Now, simplify and calculate the result:
F = 753.2 × 10^-8 N
F ≈ 7.532 × 10^-6 N (in scientific notation)
Therefore, the central force acting on the electron in the hydrogen atom is approximately 7.532 × 10^-6 N.