At temperature T , the average kinetic energy of any particle is 3 2 kT . The de Broglie wavelength follows the order:

Visible photon > thermal electron > thermal neutron.

Thermal neutron > visible photon > thermal electron.

Thermal neutron > thermal electron > visible photon.

Visible photon > thermal neutron > thermal electron.

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$4 d_{x y}$ orbital has how many ______ nodal planes.

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Important Questions on Structure of Atom

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Chemistry>Physical Chemistry>Structure of Atom>Quantum Mechanical Model of the Atom

C_{60}

emerging from a source at a speed (v) has a de Broglie wavelength of

11.0 Å

. The value of v (in m

s^{- 1}

) is closest to

[Planck's constant

h = 6.626 \times 10^{- 34} J s

]

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Chemistry>Physical Chemistry>Structure of Atom>Quantum Mechanical Model of the Atom

Which of the following pairs of

d -

orbitals will have the electron density along the axis?

HARD

Chemistry>Physical Chemistry>Structure of Atom>Quantum Mechanical Model of the Atom

Maximum number of electrons that can be accommodated in the subshell with azimuthal quantum number

l = 4

is.

HARD

Chemistry>Physical Chemistry>Structure of Atom>Quantum Mechanical Model of the Atom

The wave function,

ψ_{n, l, m_{l}}

is a mathematical function whose value depends upon spherical polar coordinates

(r, θ, ϕ)

of the electron and characterized by the quantum numbers

n, l

and

m_{l}

. Here

r

is the distance from the nucleus,

θ

is colatitude and

ϕ

is azimuth. In the mathematical functions given in the Table,

Z

is the atomic number and

a_{o}

is Bohr radius

Column 1	Column 2	Column 3
(I) $1 s$ orbital	(i) $ψ_{n, l, m_{l}} \propto {(\frac{Z}{a_{o}})}^{\frac{3}{2}} e^{- (\frac{Zr}{e_{o}})}$	(P)
(II) $2 s$ orbital	(ii) One radial node	(Q) Probability density at the nucleus $\propto \frac{1}{a_{o}^{3}}$ .
(III) $2 p_{z}$ orbital	(iii) $ψ_{n, l, m_{l}} \propto {(\frac{Z}{a_{o}})}^{\frac{5}{2}} {re}^{- (\frac{Zr}{2 a_{o}})} \cos θ$	(R) Probability density is maximum at the nucleus.
(IV) $3 d_{z}^{2}$ orbital	(iv) $xy$ -plane is a nodal plane	(S) Energy needed to excite an electron from $n = 2$ state to $n = 4$ state is $\frac{27}{32}$ times the energy needed to excite are electron from $n = 2$ state to $n = 6$ state.

For

{He}^{+}

ion, the only incorrect combination

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Chemistry>Physical Chemistry>Structure of Atom>Quantum Mechanical Model of the Atom

At temperature

T

, the average kinetic energy of any particle is

\frac{3}{2} kT

. The de Broglie wavelength follows the order:

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Chemistry>Physical Chemistry>Structure of Atom>Quantum Mechanical Model of the Atom

A stream of electrons from a heat filament was passed between two charge plates kept at a potential difference

V esu

. If

e

and

m

are charge and mass of an electron, respectively, then the value of

\frac{h}{λ}

(where

λ

is wavelength associated with the electron wave) is given by:

EASY

Chemistry>Physical Chemistry>Structure of Atom>Quantum Mechanical Model of the Atom

A metal crystallizes in a face centred cubic structure. If the edge length of its unit cell is

' a'

, the closest approach between two atoms in the metallic crystal will be

EASY

Chemistry>Physical Chemistry>Structure of Atom>Quantum Mechanical Model of the Atom

Element

B

forms ccp structure and

A

occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral voids. The structure of bimetallic oxide is:

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Chemistry>Physical Chemistry>Structure of Atom>Quantum Mechanical Model of the Atom

The correct set of four quantum numbers for the valence electrons of rubidium atom

(Z = 37)

EASY

Chemistry>Physical Chemistry>Structure of Atom>Quantum Mechanical Model of the Atom

For a 4p orbital, the number of radial and angular nodes, respectively, are

HARD

Chemistry>Physical Chemistry>Structure of Atom>Quantum Mechanical Model of the Atom

The wave function,

ψ_{n, l, m_{l}}

is a mathematical function whose value depends upon spherical polar coordinates

(r, θ, ϕ)

of the electron and characterized by the quantum numbers

n, l

and

m_{l}

. Here

r

is distance from nucleus,

θ

is colatitude and

ϕ

is azimuth. In the mathematical functions given in the Table, Z is atomic number and

a_{o}

is Bohr radius.

Column – 1	Column – 2	Column – 3
(I) $1 s$ orbital	(i) $ψ_{n, l, m_{l}} \propto {(\frac{Z}{a_{o}})}^{\frac{3}{2}} e^{- (\frac{Zr}{e_{o}})}$	(P)
(II) $2 s$ orbital	(ii) One radial node	(Q) Probability density at nucleus $\propto \frac{1}{a_{o}^{3}}$
(III) $2 p_{z}$ orbital	(iii) $ψ_{n, l, m_{l}} \propto {(\frac{Z}{a_{o}})}^{\frac{5}{2}} {re}^{- (\frac{Zr}{2 a_{o}})} \cos θ$	(R) Probability density is maximum at nucleus
(IV) $3 d_{z}^{2}$ orbital	(iv) $x y$ -plane is a nodal plane	(S) Energy needed to excite an electron from $n = 2$ state to $n = 4$ state is $\frac{27}{32}$ times the energy needed to excite electron from $n = 2$ state to $n = 6$ state.

For hydrogen atom, what is the only CORRECT combination?

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Which of the following combination of statements is true regarding the interpretation of the atomic orbitals?

(A)

An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum.

(B)

For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number.

(C)

According to wave mechanics, the ground state angular momentum is equal to

\frac{h}{2 π}

(D)

The plot of

ψ

r

for various azimuthal quantum numbers, shows peak shifting towards higher

r

value.

HARD

Chemistry>Physical Chemistry>Structure of Atom>Quantum Mechanical Model of the Atom

The wave function,

ψ_{n, l, m_{l}}

is a mathematical function whose value depends upon spherical polar coordinates

(r, θ, ϕ)

of the electron and characterized by the quantum numbers

n, l

and

m_{l}

. Here

r

is the distance from the nucleus,

θ

is colatitude and

ϕ

is azimuth. In the mathematical functions given in the Table,

Z

is the atomic number and

a_{o}

is Bohr radius

Column 1	Column 2	Column 3
(I) $1 s$ orbital	(i) $ψ_{n, l, m_{l}} \propto {(\frac{Z}{a_{o}})}^{\frac{3}{2}} e^{- (\frac{Zr}{e_{o}})}$	(P)
(II) $2 s$ orbital	(ii) One radial node	(Q) Probability density at the nucleus $\propto \frac{1}{a_{o}^{3}}$ .
(III) $2 p_{z}$ orbital	(iii) $ψ_{n, l, m_{l}} \propto {(\frac{Z}{a_{o}})}^{\frac{5}{2}} {re}^{- (\frac{Zr}{2 a_{o}})} \cos θ$	(R) Probability density is maximum at the nucleus.
(IV) $3 d_{z}^{2}$ orbital	(iv) $xy$ -plane is a nodal plane	(S) Energy needed to excite an electron from $n = 2$ state to $n = 4$ state is $\frac{27}{32}$ times the energy needed to excite are electron from $n = 2$ state to $n = 6$ state.

For the given orbital in column 1, the only correct combination for any hydrogen-like species is

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In a face centered cubic lattice atoms A are at the corner points and atoms B at the face centered points. If atom B is missing from one of the face centered points, the formula of the ionic compound is :

EASY

Chemistry>Physical Chemistry>Structure of Atom>Quantum Mechanical Model of the Atom

The quantum number of four electrons are given below: