If the wavelength of a photon is 2 . 2 × 10 - 11 m h = 6 . 6 × 10 - 34 J s , its momentum will be

1 . 452 × 10 - 44 kg . m / s .

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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Which of the following graphs of radial part of wave-function $(ψ)$ versus distance from nucleus is/are correctly labelled?

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Important Questions on Quantum Mechanical Model of Atom

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Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

Two particles

A

and

B

are in motion. If the wavelength associated with

A

33.33 nm

, the wavelength associated with

B

whose momentum is

\frac{1}{3} rd

A

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Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

Which one of the following about an electron occupying the 1s orbital in a hydrogen atom is incorrect? (The Bohr radius is represented by

a_{0}

EASY

Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

The de Broglie wavelength of an electron in the

4^{t h}

Bohr's orbit of hydrogen is:

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Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

The wavelength (in $m$ ) of a particle of mass $11.043 \times 10^{- 26} kg$ moving with a velocity of $6.0 \times 10^{7} {ms}^{- 1}$ is ______

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Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

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:

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Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

If the wavelength of a photon is

2.2 \times 10^{- 11} m (h = 6.6 \times 10^{- 34} J s)

, its momentum will be

EASY

Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

The graph between

{|ψ|}^{2}

and

r

(radical distance) is shown below. This represents:
Question Image

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Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

A proton and a

{Li}^{3 +}

nucleus are accelerated by the same potential. If

λ_{Li}

and

λ_{p}

denote the de Broglie wavelengths of

{Li}^{3 +}

and proton respectively, then the value of

\frac{λ_{Li}}{λ_{p}}

x \times 10^{- 1}

. The value of

x

is _____ (Rounded off to the nearest integer) [Mass of

{Li}^{3 +} = 8.3

mass of proton]

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Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

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?

HARD

Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

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

EASY

Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

The wavelength (in

nm

) of an electron moving with a velocity of

812 m s^{- 1}

(mass of electron

= 9.1 \times 10^{- 31} kg

and Plank's constant

= 6.626 \times 10^{- 34} Js

) is approximately _______

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Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

At temperature

T

, the average kinetic energy of any particle is

\frac{3}{2} kT

. The de Broglie wavelength follows the order:

EASY

Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

150

watt bulb emits light of wave length

6600 Å

and only

8 %

of the energy is emitted as light. How many photons are emitted by the bulb per second?

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Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

The correct statement about probability density (except at infinite distance from nucleus) is :

HARD

Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

The plots of radial distribution functions for various orbitals of hydrogen atom against '

r'

are given below.

The correct plot for $3 s$ orbital is :

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Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

A source of monochromatic radiation wavelength $400 nm$ provides $1000 J$ of energy in $10$ seconds. When this radiation falls on the surface of sodium, $x \times 10^{20}$ electrons are ejected per second. Assume that wavelength $400 nm$ is sufficient for ejection of electron from the surface of sodium metal. The value of $x$ is ______. (Nearest integer)

$(h = 6.626 \times 10^{- 34} Js)$

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Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

The wavelength of electrons accelerated from rest through a potential difference of $40 kV$ is $X \times 10^{- 12} m .$ The value of $x$ is. (Nearest integer)

Given: Mass of electron $= 9.1 \times 10^{- 31} kg$

Charge on an electron $= 1.6 \times 10^{- 19} C$

Planck's constant $= 6.63 \times 10^{- 34} Js$

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Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

The electrons are more likely to be found:
Question Image

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Chemistry>Physical Chemistry>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

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>Quantum Mechanical Model of Atom>Quantum Mechanical Model of Atom – Schrödinger Equation

P

is the probability of finding the

1 s

electron of the hydrogen atom in a spherical shell of infinitesimal thickness,

dr

, at a distance,

r

, from the nucleus. The volume of this shell is

4 π r^{2} d r

. The qualitative sketch of the dependence of

P

r

is:

Which of the following graphs of radial part of wave-function ψ versus distance from nucleus is/are correctly labelled?

Important Questions on Quantum Mechanical Model of Atom

Learn and Prepare for any exam you want !

Which of the following graphs of radial part of wave-function $(ψ)$ versus distance from nucleus is/are correctly labelled?