GATE PH 2024 Paper 1 — page 13

Questions 37–39 of 65. Imported answers require review unless explicitly marked reviewed.

The spin-orbit interaction in a hydrogen-like atom is given by the Hamiltonian

where

is a real constant. The splitting between levels

and

due to this interaction is

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the Lagrangian

. If

and

denote the generalized momenta conjugate to

and

, respectively, then the canonical equations of motion are

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The X-ray diffraction pattern of a monatomic cubic crystal with rigid spherical atoms of radius 1.56 Å shows several Bragg reflections of which the reflection appearing at the lowest

value is from (111) plane. If the wavelength of X-ray used is 0.78 Å, the Bragg angle (in

, rounded off to one decimal place) corresponding to this reflection and the crystal structure, respectively, are

Your answerChoose one option.

and body centered cubic

and face centered cubic

and body centered cubic

and face centered cubic

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

2024 · Paper 1

Question 37

Question 38

Question 39