In the Bohr model of the hydrogen atom,
the speed of the electron is approximately 2.31 × 106 m/s.Find the central force acting on the electron
as it revolves in a circular orbit of radius 4.95 × 10−11 m.
Answer in units of N.
Find the centripetal acceleration of the electron.
Answer in units of m/s2.
2.31 × 10>6 m/s (should be 10 to the 6 power) and 4.95 × 10>−11 m (should be 10 to the -11 power) answer 1.0780e23 was incorrect. Need in N.
To find the central force acting on the electron, we can use the formula for centripetal force. 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 speed of the electron, and
r is the radius of the orbit.
In this case, we are given the speed of the electron (v = 2.31 × 106 m/s) and the radius of the orbit (r = 4.95 × 10−11 m).
The mass of an electron (m) is approximately 9.11 × 10^−31 kg.
Plugging in the given values into the formula, we get:
F = ((9.11 × 10^−31 kg) * (2.31 × 10^6 m/s)^2) / (4.95 × 10−11 m)
Simplifying this equation, we find:
F = 8.23815 × 10−8 N
Therefore, the central force acting on the electron is approximately 8.23815 × 10^−8 N.
To find the centripetal acceleration of the electron, we can use the formula for centripetal acceleration. Centripetal acceleration is given by the equation:
a = v^2 / r
Where:
a is the centripetal acceleration,
v is the speed of the electron, and
r is the radius of the orbit.
In this case, we are given the speed of the electron (v = 2.31 × 106 m/s) and the radius of the orbit (r = 4.95 × 10−11 m).
Plugging in the given values into the formula, we get:
a = (2.31 × 10^6 m/s)^2 / (4.95 × 10−11 m)
Simplifying this equation, we find:
a ≈ 1.071 × 10^26 m/s^2
Therefore, the centripetal acceleration of the electron is approximately 1.071 × 10^26 m/s^2.