a.) Frist, the coulomb force is the centripetal force; set the two expressions w

Question

a.) Frist, the coulomb force is the centripetal force; set the two expressions wqual to each other and solve for mv.

b.) Secondly, the angular momentum of the orbiting electron is quantized. Set the expression for the classical angular momentum equal to nh and solve the resulting equation for r.

c.) for n=1, determine the orbital radius r. q=e=-1.6x!0^-19 C h = 1.055x10^-34Js ke 9x10^9nm^2/C^2 me=9.09x10^-31

Calculate a value for the coefficient of 1/n2 expression from the previous part. That expression is the ionization energy in terms of the quantum number n. Write the difference in energy levels (the energy of the photon emitted) in terms of h, c and A, set it equal to the expression in e) and rearrange to get the same form as Rydberg's equation 9) Calculate the coefficient in front of the difference in 1/A and compare to Rydberg's constant

Explanation / Answer

a] centripetal force = mv^2/R

and the force = Kq^2/R^2

so equating both we get

mv^2/R = Kq^2/R^2

= v = sqrt [Kq^2/Rm] -------[1]

so we need to find mv in the first part = m*  sqrt [Kq^2/Rm]

2]mvR = nh/2pi

= the orbital angular momentum of the electron is quantised as it specifically depends on the value of n and r

r = nh/2pi*mv

3]we put on the values of n , q to get the value for part c

4] as we Know from Bohrs model

radius is proportional to = n^2/Z

and V is proportional to Z/n

so we know that

E = -13.6 z^2 /n^2

so KE = +13.6 z^2/n^2

and PE = - 2KE

= -27.2 z^2 /n^2

so when we add up KE and PE it equals = the total energy = -13.6 z^2/n^2

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