6. Consider the situation of an electron rotating in circular motion around a proton. The positionvector of the electron on the circle is related to the cartesian base vectors via:r = rcos(0)x + rsin(0)ŷ = rcos(wt)â+ rsin(wt)ŷWhere 0 is the angle above the x-axis, that the electron has passed over.re= pt(a) Calculate the velocity v =drand acceleration a =dtdvand their absolute values.dtExpress the acceleration in terms of the velocity. (result for checking and for furtherv².calculation: a =r(b) Use Newton's law (F = ma) to calculate the corresponding centripetal force. Thecentripetal force should be balanced with the Coulomb force to keep the electron on thecircle around the proton. In the first shell, the electron moves around the proton at adistance of r = 5.29 × 10-11 m. Calculate the required velocity to keep the electronon a force-balanced ride around the proton.

Answered: Image /qna-images/answer/3b1f4068-a4f5-4ff7-bdce-2ec59698e25d.jpg

Answered: (a) Calculate the velocity v = dr and…

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