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

Question

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) Is orbital (i) ψ n , l , m l ∝ Z a o 3 2 e - Zr e o (P) (II) 2s orbital (ii) One radial node (Q) Probability density at nucleus ∝ 1 a o 3 (III) 2 p z orbital (iii) ψ n , l , m l ∝ Z a o 5 2 re - 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 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?

TestHub · Accepted Answer

We have to select only correct combination hence, the option (iv) is correct.

For 1s orbital : $ψ_{n, l, m} α {(\frac{Z}{a_{0}})}^{\frac{3}{2}} e^{\frac{- zr}{a_{0}}}$

Energy needed to excite an electron : from $n = 2$ to $n = 4$

${ΔE}_{2 - 4} = 13 .6 Z^{2} \times \frac{3}{16} eV$

Energy needed to excite an electron : from $n = 2$ to $n = 6$

${ΔE}_{2 - 6} = 13 .6 Z^{2} \times \frac{8}{36}$

${ΔE}_{2 - 4} = \frac{27}{32} E_{2 - 6}$ (hence, true)

Chemistry - Atomic Structure Question with Solution | TestHub

Options:

Doubts & Discussion

Column – 1	Column – 2	Column – 3
(I) Is orbital	(i) $ψ_{n, l, m_{l}} \propto {(\frac{Z}{a_{o}})}^{\frac{3}{2}} e^{- (\frac{Zr}{e_{o}})}$	(P)
(II) 2s 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.