The wave function -n-l-m is a mathematical function whose value depends upon spherical polar coordinates r- - - of the electron and characterized by the quantum numbers n- l and ml- Here r is distance from nucleus- - is colatitude and - is azimuth- In the mathematical functions given in the table- Z is atomic number and a0 is Bohr radius-For He- ion- the only INCORRECT combination is

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Introduction to Quantum Mechanical Model

The wave func...

Question

The wave function $ψ_{n, l, m}$ 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 $a_{0}$ is Bohr radius.

For $H e^{+}$ ion, the only INCORRECT combination is

(II) (ii) (Q)

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(I) (i) (S)

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(I) (i) (R)

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(I) (iii) (R)

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Solution

The correct option is D (I) (iii) (R)
1s orbital cannot have $θ$ function (angular function).
Therefore d) is incorrect.

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Similar questions

Q. The wave function

ψ_{n, l, m}

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_{0}

is Bohr radius.

For

H e^{+}

ion, the only INCORRECT combination is

Q. The wave function

ψ_{n, l, m}

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_{0}

is Bohr radius.

For

H e^{+}

ion, the only INCORRECT combination is

The wave function, $Ψ_{n, l, m_{l}}$ is a methematical function whose value depends upon spherical polar coordinates (r, θ, Ф) of the electron and characterized by the quantum numbers n, l and m. Here r is distance from nucleus, θ is colatitude and Ф is azimuth. In the mathematical functions given in the Table, Z is atomic number and $a_{0}$ is Bohr radius.

Column 1	Column 2	Column 3
(i) 1s orbital	(i) $Ψ_{n, l, m_{l}} \propto {(\frac{Z}{a_{0}})}^{\frac{3}{2}} e^{(\frac{- Z r}{a_{0}})}$	(P)
(ii) 2s orbital	(ii) One radial node	(Q) Probability density at nucleus $\propto \frac{1}{a_{0}^{3}}$
(iii) 2 $p_{z}$ orbital	(iii) $Ψ_{n, l, m_{l}} \propto {(\frac{Z}{a_{0}})}^{\frac{5}{2}} r e^{(\frac{- Z r}{2 a_{0}})} c o s θ$	(R) Probability density is maximum at nucleus
(iv) 3 $d_{z}^{2}$ orbital	(iv) xy-plane is a nodal plane	(S) Energy needed to excite 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 $H e^{+}$ ion, the only INCORRECT combination is:

Column 1	Column 2	Column 3
(i) 1s orbital	(i) $Ψ_{n, l, m_{l}} \propto {(\frac{Z}{a_{0}})}^{\frac{3}{2}} e^{(\frac{- Z r}{a_{0}})}$	(P)
(ii) 2s orbital	(ii) One radial node	(Q) Probability density at nucleus $\propto \frac{1}{a_{0}^{3}}$
(iii) 2 $p_{z}$ orbital	(iii) $Ψ_{n, l, m_{l}} \propto {(\frac{Z}{a_{0}})}^{\frac{5}{2}} r e^{(\frac{- Z r}{2 a_{0}})} c o s θ$	(R) Probability density is maximum at nucleus
(iv) 3 $d_{z}^{2}$ orbital	(iv) xy-plane is a nodal plane	(S) Energy needed to excite 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 $H e^{+}$ ion, the only INCORRECT combination is:

Q. For any two real numbers

θ

ϕ

, we define

θ R ϕ

if and only if

{sec}^{2} θ - {tan}^{2} ϕ = 1

. The relation

R

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The correct option is D (I) (iii) (R)1s orbital cannot have θ function (angular function). Therefore d) is incorrect.

The correct option is D (I) (iii) (R)
1s orbital cannot have $θ$ function (angular function).
Therefore d) is incorrect.