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The number of regions of maximum probability is one for

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Important Questions on Structure of Atom

EASY

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

The orbital with

4

radial and

1

angular nodes is

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

A certain orbital has

n = 4

and

m_{l} = - 3 .

The number of radial nodes in this orbital is _______. (Round off to the Nearest Integer).

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

An orbital with one angular node shows three maxima in its radial probability distribution curve, the orbital is

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

The number of radial nodes, angular nodes of a

4 f -

orbital are respectively

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

The number of angular nodes and radial nodes in

3 s

orbital are

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

The number of radial and angular nodes in

4 d

orbital are, respectively

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

A certain orbital has no angular nodes and two radial nodes. The orbital is:

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

The electrons are more likely to be found:
Question Image

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

The number of regions, where the probability density of electrons is reduced to zero for

3 s

atomic orbital is

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

How many of the following orbitals have two angular and one radial nodes?

$3 d; 4 d; 5 f; 3 p$

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

The number of atomic orbitals from the following having

5

radial nodes is

7 s, 7 p, 6 s, 8 p, 8 d

HARD

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

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:

EASY

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

The correct order of total number of node of atomic orbitals is _______

HARD

Chemistry>Physical Chemistry>Structure of Atom>Towards 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.