Does anybody know how I can find the mass of the electron for this question. I need to find it first to solve for the real one but don't see mass anywhere in the question.I see radiant and speed but no mass The radius of circular electron orbits in the Bohr model of the hydrogen atom are given by (5.29 ✕ 10−11 m)n2, where n is the electron's energy level (see figure below). The speed of the electron in each energy level is (c/137n), where c = 3 ✕ 108 m/s is the speed of light in vacuum.
The best thing to do would be to equate the electrostatic force of attraction and the centripetal force.
(m*v^2)/r = k*(e*e/r^2)
Where m = mass of electron
v = velocity
e = charge on electron (and on hydrogen nucleus)
r = radius of orbit
k = 1/4πƐ = 9 * 10^9
9.11E-31 Kg ... from google
the speeds are not close enough to c to worry about relativistic effects
Ah, my bad, I thought you had to solve for 'm' in the question.
To find the mass of the electron in this question, we can use the formula for the centripetal force experienced by the electron in its circular orbit:
F = (mv^2) / r
where:
F = centripetal force
m = mass of the electron
v = speed of the electron
r = radius of the orbit
In the Bohr model, the centripetal force is provided by the electrostatic attraction between the electron and the nucleus:
F = (e^2) / (4πε₀r)
where:
e = charge of the electron
ε₀ = permittivity of free space
r = radius of the orbit
We can equate these two expressions for F and solve for m:
(mv^2) / r = (e^2) / (4πε₀r)
Rearranging the equation, we get:
m = (e^2) / (4πε₀v^2)
To substitute the values given in the question, we need to know the charge of the electron. The charge of an electron is approximately -1.602 x 10^-19 Coulombs.
Now, let's put the values in the equation:
m = ((-1.602 x 10^-19 C)^2) / (4πε₀(3 x 10^8 m/s)^2)
To evaluate this further, we need to know the value of ε₀. The value of ε₀ is approximately 8.854 x 10^-12 C²/Nm².
Substituting this value into the equation:
m = ((-1.602 x 10^-19 C)^2) / (4π(8.854 x 10^-12 C²/Nm²)(3 x 10^8 m/s)^2)
Evaluating this expression will give us the mass of the electron.
I hope this explanation helps you understand how to find the mass of the electron in this question.