GATE PH format:nat PYQs & Answers — Page 8

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Questions 71–80 of 182. Imported answers require independent review unless marked reviewed.

Topic practice 182 questionsPage 8 of 19

Three non-interacting bosonic particles of mass

each, are in a one-dimensional infinite potential well of width

. The energy of the third excited state of the system is

. The value of

(in integer) is ______.

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The spacing between two consecutive S-branch lines of the rotational Raman spectra of hydrogen gas is 243.2 cm

. After excitation with a laser of wavelength 514.5 nm, the Stoke’s line appeared at 1761.1 cm

for a particular energy level. The wavenumber (rounded off to the nearest integer), in cm

, at which Stoke’s line will appear for the next higher energy level is ______.

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The transition line, as shown in the figure, arises between

and

states without any external magnetic field. The number of lines that will appear in the presence of a weak magnetic field (in integer) is ______.

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Consider the atomic system as shown in the figure, where the Einstein A coefficients for spontaneous emission for the levels are

and

. If

atoms/cm

are excited from level 0 to level 2 and a steady state population in level 2 is achieved, then the steady state population at level 1 will be

. The value of

(in integer) is ______.

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and

are constant vectors,

and

are generalized positions and conjugate momenta, respectively, then for the transformation

and

to be canonical, the value of

(in integer) is ______.

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A linear charged particle accelerator is driven by an alternating voltage source operating at 10 MHz. Assume that it is used to accelerate electrons. After a few drift-tubes, the electrons attain a velocity 2.9 × 10^8 m s⁻¹. The minimum length of each drift-tube, in m, to accelerate the electrons further (rounded off to one decimal place) is _____.

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The Coulomb energy component in the binding energy of a nucleus is 18.432 MeV. If the radius of the uniform and spherical charge distribution in the nucleus is 3 fm, the corresponding atomic number (rounded off to the nearest integer) is _____.

(Given:

MeV fm)

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For a two-nucleon system in spin singlet state, the spin is represented through the Pauli matrices

for particles 1 and 2, respectively. The value of

(in integer) is _____.

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A contour integral is defined as

where

is a positive integer and

is the closed contour, as shown in the figure, consisting of the line from −100 to 100 and the semicircle traversed in the counter-clockwise sense.

The value of

(in integer) is _____.

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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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GATE PH format:nat PYQs

Question 21

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Question 23

Question 24

Question 25

Question 47

Question 48

Question 49

Question 50

Question 51