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.
A) Is equilibrium position of the electron at the center of the nucleus?
B)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 r⃗ , R, e, and constants π and ϵ0.
C) Calculate the frequency of oscillation. Express your answer in terms of the variables m, R, e, and constants π and ϵ0.

In 1897 Thomson determined the electron and then went directly to endorse a model for the structure of the atom. His work additionally led to the discovery of the mass spectrograph. The British physicist Joseph John (J. J.)J.J. Thomson's experiments with cathode ray tubes confirmed that every atom comprises tiny negatively charged subatomic debris or electrons. Thomson proposed the plum pudding version of the atom, which had negatively-charged electrons embedded within an undoubtedly-charged "soup."

Thomson, at some stage in a lecture on the Royal group in London, on 30 April 1897. “The atoms of the everyday factors are made up of corpuscles and holes, the holes being predominant,” he endured. Thomson described his experiments with cathode rays to verify the lifestyles of those subatomic corpuscles.

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