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2. This question is about the Bohr model of the hydrogen atom and the Heisenberg uncertainty principle. In the nth energy state, the hydrogen atom has energy E, and the electron orbits with speed v, in an orbit of radius . En, Yn and Vn are given by the following relationships. En 13.606 eV n rn=0.0529n² nm (a) Apply the expressions above, to hydrogen in its ground state, to determine the ground state energy and the radius of the electron orbit. (b) Determine the speed of the electron in the ground state using the quantization of angular momentum in the Bohr model of the hydrogen atom and the radius determined from part (a).
(c) According to the Schrödinger model, the position and the speed of an electron are not well defined. It can be assumed that the uncertainty in the position of the electron in a hydrogen atom is equal to the radius of the electron orbit in the n= 1 state. (i) Apply the Heisenberg uncertainty principle to hydrogen in this state to show that the uncertainty in the speed of the electron is approximately equal to the electron speed as calculated in (b). (ii) = Determine the time spent for an electron that spontaneously jumps from an n=1 to an n= 4 state.