The wave function - n - l - m is a mathematical function whose value depends upon spherical polar coordinates r - - - of the electron and characterizedby the quantum numbers n - 1 and m 1- Here r is distance from nucleus- - is colatitude and - is azimuth- In the mathematical functions given in the table-Z is atomic number and a 0 is Bohr radius-For He -ion- the only INCORRECT combination isA- II ii QB- I i SC- I i RD- I iii R

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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 the given orbital in Column-I, the only CORRECT combination for any hydrogen-like species 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. Type of terms and corresponding number is written in Column 2 and Column 3 respectively of the Binomial in Column 1.

\begin{matrix} C o l u m n I & C o l u m n I I & C o l u m n 3 (I) & {(5^{\frac{1}{6}} + 7^{\frac{1}{9}})}^{1824} & (i) & T o t a l n u m b e r o f r a t i o n a l t e r m s & (P) & 4 (I I) & {(5^{\frac{1}{6}} + 2^{\frac{1}{8}})}^{100} & (i i) & T o t a l n u m b e r o f i r r a t i o n a l t e r m s & (Q) & 102 (I I I) & {(3^{\frac{1}{4}} + 4^{\frac{1}{3}})}^{99} & (i i i) & \frac{1}{2} [\frac{T o t a l n u m b e r o f t e r m s}{N u m b e r o f r a t i o n a l t e r m s}], & (R) & 224 w h e r e [.] r e p r e s e n t s g r e a t e s t i n t e g e r f u n c t i o n . (I V) & {(7^{\frac{1}{3}} + 11^{\frac{1}{9}})}^{2007} & (i v) & T o t a l n u m b e r o f t e r m s & (S) & I s d i v i s i b l e b y 13 \end{matrix}

Select the incorrect combination

Q. A function is defined as

f (x) = a^{x} \forall ϵ R

and 0 < a < 1, then which of the following is true ?
(i) It is an increasing function
(ii) It is an decreasing function
(iii) All such functions must meet at (0, 1)

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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.