In the Bohr model of the hydrogen atom, the speed of the electron is approximately 2.45 × 106 m/s.
Find the central force acting on the electron as it revolves in a circular orbit of radius 5.18 × 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:
Fc = (m*v^2) / r
where Fc 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.
From the problem, we are given:
- Speed of the electron (v) = 2.45 × 10^6 m/s
- Radius of the circular orbit (r) = 5.18 × 10^(-11) m
The mass of an electron is approximately 9.10938356 × 10^(-31) kg.
Now, we can substitute these values into the centripetal force formula to find the central force acting on the electron:
Fc = (m * v^2) / r
Fc = (9.10938356 × 10^(-31) kg * (2.45 × 10^6 m/s)^2) / (5.18 × 10^(-11) m)
Calculating this expression gives us:
Fc = 9.10938356 × 10^(-31) kg * (2.45 × 10^6 m/s)^2 / (5.18 × 10^(-11) m)
Fc = 1.096718623 × 10^(-17) kg·m/s^2 / m
Fc = 1.096718623 × 10^(-17) N
Therefore, the central force acting on the electron in the Bohr model of the hydrogen atom is approximately 1.096718623 × 10^(-17) N.
To find the central force acting on the electron in the Bohr model, 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 circular orbit
Given:
v = 2.45 × 10^6 m/s
r = 5.18 × 10^-11 m
First, we need to find the mass of the electron. The mass of an electron is approximately 9.11 × 10^-31 kg.
Now, we can calculate the central force:
F = (9.11 × 10^-31 kg) * (2.45 × 10^6 m/s)^2 / (5.18 × 10^-11 m)
Calculating the expression:
F ≈ 9.11 × 10^-31 kg * (2.45 × 10^6 m/s)^2 / (5.18 × 10^-11 m)
F ≈ 4.38 × 10^-9 N
Therefore, the central force acting on the electron in the Bohr model is approximately 4.38 × 10^-9 N.