The wave function, \psi_{ n , 1, m_{ l }} is a mathematical function whose value depends upon spherical polar coordinates ( r , heta, \phi) of the electron and characterized by the quantum numbers n , 1 and m _{ l }. Here r is the distance from the nucleus, heta is colatitude and \phi is azimuth. In the mathematical functions given in the Table, Z is the atomic number and a_0 is Bohr radiusColumn 1Column 2Column 3(I) 1s orbital ext {(i) } \psi_{ n , 1, m_1} \propto\left(\frac{ Z }{ a _{ o }} ight)^{\frac{3}{2}} e ^{-\left(\frac{ Zr }{ e _{ o }} ight)}(P) (II) 2s orbital(ii) One radial node(Q) Probability density at the nucleus \propto \frac{1}{ a _{ o }^3}.(III) 2 p _{ z } orbital ext {(iii) } \psi_{ n }, 1, m_{ l } \propto\left(\frac{ Z }{ a _{ o }} ight)^{\frac{5}{2}} re ^{-\left(\frac{ Zr }{2 a _{ o }} ight)} \cos heta(R) Probability density is maximum at the 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 are electron from n =2 state to n =6 state.For ext{He} ^{+}ion, the only incorrect combination

Question

The wave function, \psi_{ n , 1, m_{ l }} is a mathematical function whose value depends upon spherical polar coordinates ( r , 	heta, \phi) of the electron and characterized by the quantum numbers n , 1 and m _{ l }. Here r is the distance from the nucleus, 	heta is colatitude and \phi is azimuth. In the mathematical functions given in the Table, Z is the atomic number and a_0 is Bohr radiusColumn 1Column 2Column 3(I) 1s orbital	ext {(i) } \psi_{ n , 1, m_1} \propto\left(\frac{ Z }{ a _{ o }}ight)^{\frac{3}{2}} e ^{-\left(\frac{ Zr }{ e _{ o }}ight)}(P) (II) 2s orbital(ii) One radial node(Q) Probability density at the nucleus \propto \frac{1}{ a _{ o }^3}.(III) 2 p _{ z } orbital	ext {(iii) } \psi_{ n }, 1, m_{ l } \propto\left(\frac{ Z }{ a _{ o }}ight)^{\frac{5}{2}} re ^{-\left(\frac{ Zr }{2 a _{ o }}ight)} \cos 	heta(R) Probability density is maximum at the 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 are electron from n =2 state to n =6 state.For 	ext{He} ^{+}ion, the only incorrect combination

Accepted Answer

(C) (I)&#160;(iii)&#160;(R)

Answer

(A) (I)&#160;(i)&#160;(S)

Answer

(B) (I)&#160;(i)&#160;(R)

Answer

(D) (II)&#160;(ii)&#160;(Q)

Answer & Solution

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Column 1	Column 2	Column 3
(I) 1s orbital	\(\text {(i) } \psi_{ n , 1, m_1}\) \(\propto\left(\frac{ Z }{ a _{ o }}\right)^{\frac{3}{2}} e ^{-\left(\frac{ Zr }{ e _{ o }}\right)}\)	(P)
(II) 2s orbital	(ii) One radial node	(Q) Probability density at the nucleus \(\propto \frac{1}{ a _{ o }^3}\).
(III) \(2 p _{ z }\) orbital	\(\text {(iii) } \psi_{ n }, 1, m_{ l }\) \(\propto\left(\frac{ Z }{ a _{ o }}\right)^{\frac{5}{2}} re ^{-\left(\frac{ Zr }{2 a _{ o }}\right)} \cos \theta\)	(R) Probability density is maximum at the 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 are electron from \(n =2\) state to \(n =6\) state.