In the early years of the 20th century, a leading model of the structure of the
ID: 1323283 • Letter: I
Question
In the early years of the 20th century, a leading model of the structure of the atom was that of the English physicist J. J. Thomson (the discoverer of the electron). In Thomson's model, an atom consisted of a sphere of positively charged material in which were embedded negatively charged electrons, like chocolate chips in a ball of cookie dough. Consider such an atom consisting of one electron with mass m and charge ?e, which may be regarded as a point charge, and a uniformly charged sphere of charge +e and radius R.
In Thomson's model, it was assumed that the positive material provided little or no resistance to the motion of the electron. If the electron is displaced from equilibrium by a distance r less than R, find the net force on the electron.
Express your answer in terms of the variables r? , R, e, and constants ? and ?0.
Explanation / Answer
The easiest way to get the frequency is to compare your eq with that of Hook's Law ;
F = - Kr
ma = - Kr
a = - (K/m)r
d^2r/dt^2 = - (K/m)r
It is known, by solving the differential eq above, that the frequency of the resulting harmonic motion is;
w = SqRt(K/m) rad/sec
So just compare eqs and replace "K" by the appropiate constants in your force eq.
PS: You can get fancy here by treating "r" as a vector, but I think they have in mind a one dimensional problem. So you can think of "r" as a one dimensional scalar variable, like "x". Although getting fancy will still give you the same frequency.