In the Bohr model of the hydrogen atom,
the speed of the electron is approximately
2.41 × 106 m/s.
Find the central force acting on the electron
as it revolves in a circular orbit of radius
5.15 × 10−11 m. Answer in units of N.
Find the centripetal acceleration of the elec-
tron. Answer in units of m/s2.
Use the formula for centripetal acceleration is a circular orbit, or radius R:
a = V^2/R
They have already told you the values of V and R to use.
The units of a will be m^2/s
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, which is given by:
F = (m * v^2) / r
where F is the force, m is the mass of the object (in this case, the electron), v is the velocity of the object, and r is the radius of the circular orbit.
In this case, we are given the speed of the electron, which is 2.41 × 10^6 m/s, and the radius of the orbit, which is 5.15 × 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.
Substituting these values into the centripetal force formula:
F = (9.11 × 10^(-31) kg * (2.41 × 10^6 m/s)^2) / (5.15 × 10^(-11) m)
Calculating this expression:
F ≈ 2.56 × 10^(-8) N
Therefore, the central force acting on the electron is approximately 2.56 × 10^(-8) N.
To find the centripetal acceleration of the electron, we can use the formula for centripetal acceleration, which is given by:
a = v^2 / r
where a is the acceleration, v is the velocity of the object, and r is the radius of the circular orbit.
In this case, we are given the speed of the electron, which is 2.41 × 10^6 m/s, and the radius of the orbit, which is 5.15 × 10^(-11) m.
Substituting these values into the centripetal acceleration formula:
a = (2.41 × 10^6 m/s)^2 / (5.15 × 10^(-11) m)
Calculating this expression:
a ≈ 1.14 × 10^23 m/s^2
Therefore, the centripetal acceleration of the electron is approximately 1.14 × 10^23 m/s^2.