In the Bohr model of the hydrogen atom,
the speed of the electron is approximately
2.41 × 10^6 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 electron. Answer in units of m/s^2.
To find the central force acting on the electron, you can use the formula for centripetal force:
F = (m * v^2) / r
Where:
F = Central force
m = Mass of the electron
v = Velocity of the electron
r = Radius of the circular orbit
In this case, we need to use the mass of the electron, which is approximately 9.10938356 × 10^-31 kg. The velocity of the electron is given as 2.41 × 10^6 m/s, and the radius of the orbit is given as 5.15 × 10^-11 m.
Plugging these values into the formula, we get:
F = ((9.10938356 × 10^-31 kg) * (2.41 × 10^6 m/s)^2) / (5.15 × 10^-11 m)
Calculating this expression gives us:
F ≈ 7.37 × 10^-8 N
Therefore, the central force acting on the electron is approximately 7.37 × 10^-8 N.
To find the centripetal acceleration of the electron, you can use the formula:
a = v^2 / r
Where:
a = Centripetal acceleration
v = Velocity of the electron
r = Radius of the circular orbit
Using the given values, we have:
a = (2.41 × 10^6 m/s)^2 / (5.15 × 10^-11 m)
Calculating this expression gives us:
a ≈ 1.12 × 10^24 m/s^2
Therefore, the centripetal acceleration of the electron is approximately 1.12 × 10^24 m/s^2.
F = k q1 q2 / r^2
k = 9*10^9
q1 = -1.6 * 10^-19
q2 = +1.6 * 10^-19
R = 5.15*10^-11
SO
F = -9*10^9 * 1.6^2 * 10^-38 / 5.15^2*10^-22
=-.869*10^-7 N = -8.69*10^-8 N
negative r is inward direction
v^2/r = -(2.41)^2*10^12/5.15*10^-11
=-1.13*10^23
also acceleration inward toward center
rough check
does F = ma?
F = -8.69 * 10^-8
m a = 9.11*10^-31 *-1.13*10^23 = -10.3 *10^-8
off by about 15%. Not too bad for a rough estimate