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 formula for centripetal force (Fc) which is given by:
Fc = (m * v²) / r
Where:
- Fc is the centripetal force
- m is the mass of the electron
- v is the speed of the electron
- r is the radius of the circular orbit
In this case, we are given the speed of the electron as 1.97 × 10^6 m/s and the radius of the circular orbit as 4.72 × 10^(-11) m.
First, let's find the mass of the electron. The mass of an electron is approximately 9.11 × 10^(-31) kg.
Now, let's substitute the given values into the centripetal force formula:
Fc = (9.11 × 10^(-31) kg * (1.97 × 10^6 m/s)²) / (4.72 × 10^(-11) m)
Calculating this expression gives us:
Fc = 7.59 × 10^(-8) N
Therefore, the central force acting on the electron is approximately 7.59 × 10^(-8) N.