GATE PH 2025 Paper 1 — page 11

Questions 31–33 of 65. Imported answers require review unless explicitly marked reviewed.

A linear dielectric sphere of radius

has a uniform frozen-in polarization along the

-axis. The center of the sphere initially coincides with the origin, about which the electric dipole moment is

. When the sphere is shifted to the point

, the corresponding dipole moment with respect to the origin is

. The value of

(in integer) is ______

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The effective magnetic moment (in units of Bohr magneton) for the ground state of an isolated

ion with 6 unpaired electrons in the

shell according to Hund’s rules is (in integer) _____

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Powder X-ray diffraction pattern of a cubic solid with lattice constant

has the (111) diffraction peak at

. If the lattice expands such that the lattice constant becomes

, the angle (in degrees) corresponding to the (111) peak changes to

. The value of

(rounded off to one decimal place) is _____

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2025 · Paper 1