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 the given orbital in Column-I- the only CORRECT combination for any hydrogen-like species is-

You visited us 11 times! Enjoying our articles? Unlock Full Access!

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 the given orbital in Column-I, the only CORRECT combination for any hydrogen-like species is:

(IV) (iv) (R)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(II) (ii) (P)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(III) (iii) (P)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(I) (ii) (S)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B (II) (ii) (P)
Number of radial nodes = $(n - l - 1)$

Along the radius is a spherical node

Number of angular nodes = $l$

So for a 2s orbital,

Number of radial nodes = $(2 - 0 - 1) = 1$

So the wavefunction of 2s has one radial node and the graph of the wave function vs radius is given below, with one point where the wavefuction changes from +ve to -ve.

Suggest Corrections

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 hydrogen atom, the only CORRECT 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. Assertion :In hydrogen and hydrogen like species, orbital energy depends only on the quantum number n whereas in multi-electron atom it depends on quantum numbers n and l. Reason: The principal quantum number determines the size and the energy of the orbital.

Q. For the given orbital in Column I, the only CORRECT combination for any hydrogen-like species is

Join BYJU'S Learning Program