Question

According to the classical model of the hydrogen atom, an electron moving in a circular orbit with a radius of 0.053 nm around a proton fixed in the center is unstable, and the electron must eventually fall on the proton. Estimate the time it takes for an electron to fall on a proton

Answer 1

F = GmM/R^2 = ma => GM/R^2 = a

G= 6.67x10^-11

M proton = 1.67x10^-27

m Electron = 9.11 x10^-31

R = 0.053 x 10^-9

a = -2.10167…x10^-27

a = -2.1017x10^-27

Treat "a" as gravity, because the electron is like free falling on the proton, that’s why it is expressed as negative.

Change in Distance = vi(t) + at

-0.053x10^-19 = 0 + -2.1017x10^-27 (t)

t = 521768.092 secs or 520000 secs <== sig fig