The uranyl ion, [UO;]?", is a ubiquitous structural motif in U(VI) chemistry. The molecule is linear and the U-O bond length is approximately 2Å. When lying along the z-axis, the coordinates of uranyl can be specified by: ry = 0; TOA =0: To a) Define a 3 x 3 matrix representing a reflection in the xy-plane and show that uranyl is symmetric with respect to this symmetry operation b) Define a 3 x 3 matrix representing an arbitrary rotation of 0 radians about the z-axis and show that the uranyl molecule is symmetric with respect to this symmetry operation c) What is the point group of the uranyl molecule?

The uranyl ion, [UO;]?", is a ubiquitous structural motif in U(VI) chemistry. The molecule is linear and the U-O bond length is approximately 2Å. When lying along the z-axis, the coordinates of uranyl can be specified by: ry = 0; TOA =0: To a) Define a 3 x 3 matrix representing a reflection in the xy-plane and show that uranyl is symmetric with respect to this symmetry operation b) Define a 3 x 3 matrix representing an arbitrary rotation of 0 radians about the z-axis and show that the uranyl molecule is symmetric with respect to this symmetry operation c) What is the point group of the uranyl molecule?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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