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Question: 1 a describe the 1927 experiment of phipps and taylor...

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1. (a Describe the 1927 experiment of Phipps and Taylor dealing with hydrogen atoms in a Stern-Gerlach apparatus. Explain in detail why the results of the experiment require the introduction of a fourth quantum number in addition to n, E and m to describe the hydrogen atom. (4 marks) (b) The Pauli Matrices in the s, basis are: 0 -1 and the operators representing an electrons spin components are s-thơ whereix, y, z. , A spin half particle which is initially described by the un-normalised state vector n the s, basis, is passed into and traverses a Stern-Gerlach analyser whose magnetic field is oriented in the z-direction. (i) What are the possible states of the particle at the output of the analyser? Calculate (ii) Subsequently, the particle is passed into and traverses a second Stern-Gerlach the probability that each output state will be observed, and explain your reasoning (2 marks) analyser whose magnetic field is oriented in the x-direction. What are the possible states of the particle at the output of the second analyser? Calculate the probability that each state will be observed, and explain your reasoning. (2 marks) Comment briefly on how the possible results of this sequence of observations illustrates the fundamental meaning of the uncertainty principle (iii) (2 marks)

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