▶ A non-relativistic particle of mass m is held in a circular orbit around the origin by an attractive force f (r) = −kr where k is a positive constant

(a) Show that the potential energy can be written U(r) = kr^2/2 Assuming U(r) = 0 when r = 0

(b) Assuming the Bohr quantization of the angular momentum of the particle, show that the radius r of the orbit of the particle and speed v of the particle can be writte

where n is an integer

(c) Hence, show that the total energy of the particle is

(d) If m = 3 × 10^(−26) kg and k = 1180 Nm^(−1), determine the wavelength of the photon in nm which will cause a transition between successive energy levels.