GATE PH year:2021 PYQs & Answers — Page 7

Questions 61–65 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 7 of 7

The normalized radial wave function of the second excited state of hydrogen atom is

where

is the Bohr radius and

is the distance from the center of the atom. The distance at which the electron is most likely to be found is

. The value of

(in integer) is _____.

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Consider an atomic gas with number density

m⁻³, in the ground state at 300 K. The valence electronic configuration of atoms is

. The paramagnetic susceptibility of the gas

. The value of

(rounded off to two decimal places) is _____.

(Given: Magnetic permeability of free space

H m⁻¹

Bohr magneton

A m²

Boltzmann constant

J K⁻¹)

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Consider a cross-section of an electromagnet having an air-gap of 5 cm as shown in the figure. It consists of a magnetic material (

) and is driven by a coil having

A, where

is the number of turns and

is the current in Ampere.

Ignoring the fringe fields, the magnitude of the magnetic field

(in Tesla, rounded off to two decimal places) in the air-gap between the magnetic poles is _____.

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The spin

and orbital angular momentum

of an atom precess about

, the total angular momentum.

precesses about an axis fixed by a magnetic field

, where

is a constant. Now the magnetic field is changed to

. Given the orbital angular momentum quantum number

and spin quantum number

is the angle between

and

for the largest possible values of total angular momentum quantum number

and its z-component

. The value of

(in degree, rounded off to the nearest integer) is _____.

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The spin-orbit effect splits the

transition (wavelength,

Å) in Lithium into two lines with separation of

Å. The corresponding positive value of energy difference between the above two lines, in eV, is

. The value of

(rounded off to the nearest integer) is _____.

(Given: Planck’s constant,

eV s

Speed of light,

m s⁻¹)

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GATE PH year:2021 PYQs

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