Quantum Chemistry - 2 - GATE Chemistry MCQ

A perturbation  is introduced in a box of width 1 unit, where V₀ is ( << 1 ) is a positive constant. The first order energy correction to the first exited state is α V₀ . The value of α is_________

σ_x , σy and σ_z  are the Pauli m atrices. The expression is equal to 2σ_x σ_y + σ_y σ_x is equal to 

For linear momentum vector operator  -and position vector operator   the operator  is equivalent to

The degeneracy of the n = 2 level for a three dimensional isotropic oscillator is ________. (an integer)

The operation of the commutator  on a function f ( x ) is equal to

The degeneracy of a quantum particle in a cubic box having energy three times that of the lowest energy is ________

Consider a normalized molecular orbital  constructed from two different atomic orbitals  and  that fonn an orthonormal set. Here i = √-1. The value of |c|² is ______ (upto one decim al place)

The normalized wavefiinctions ψ₁ and ψ₂ correspond to the ground state and the first excited states of a particle in a potential. The operator A acts on the wavefiinctions as The expectation value of the operator A for the state is ________. (upto two decimal places)

Three identical non- interacting particles, each of spin 1/2 and mass m. are moving in a one-dimensional infinite potential well given by

the energy of the lowest energy state of the system is:

A certain 2-level system lias stationary state energy  with normalized wave functions
 respectively. A small perturbation V is applied on the system such that V₁₂ = 2. The wavefunction of the particle in groimd state collected upto first order, will be

Given that work function of a metal is 5 eV and that photons of 9 eV are incident on it. the maximum velocity of emitted electrons is approximately______ x10⁶ m/s (upto one decimal place)

For a system of two spin -1/2 particles, the value 0f 

The ground state wave function of hydrogen atom is given by where a₀ is the Bohr
radius. The plot of the radial probability density P(r) for the hydrogen atom in the ground state is

A particle of mass m is constrained to move in a circular ring of radius R . When a perturbation

(where a is a real constant) is added, the first order collection to the ground state energy is The value
of η is ______ (up to one decimal place)

The wavefiuiction for a linear harmonic oscillator described by N where α and N are constants, has

The ‘‘trial'’ wavefuction for He atom is taken as where N is the normalization factor and Z ' is the variational parameter. Expression for the energy in terms of Z ' is found to be

Then the lowest value of the energy ( E ') for He atom i s _________________(in a.u .)
(Round off to two decimal places)

The average distance between the electron and nucleus of a He⁺ (singly ionised Heliumion) in the 1s state is