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The angular momentum of electrons in d orbital is equal to

\sqrt{6} h

\sqrt{2} h

2 \sqrt{3} h

0 h

The correct order of total number of node of atomic orbitals is:

4f > 6s > 5d
6s > 5d > 4f
4f > 5d > 6s
5d > 4f > 6s

Which of the following statement is correct?

Number of angular nodes = n-l-1
Number of radial nodes = l
Total number of nodes = n-1
All

Maximum number of total nodes is present in:

5s
5p
5d
All have same number of nodes

Which of the following orbitals has two spherical nodes?

2s
4s
3d
6f

The correct Schrodinger's wave equation for a electron with total energy E and potential energy V is given by

\frac{\partial^{2} ψ}{\partial x^{2}} + \frac{\partial^{2} ψ}{\partial y^{2}} + \frac{\partial^{2} ψ}{\partial z^{2}} + \frac{8 π^{2}}{{mh}^{2}} (E - V) ψ = 0

\frac{\partial^{2} ψ}{\partial x^{2}} + \frac{\partial^{2} ψ}{\partial y^{2}} + \frac{\partial^{2} ψ}{\partial z^{2}} + \frac{8 πm}{h^{2}} (E - V) ψ = 0

\frac{\partial^{2} ψ}{\partial x^{2}} + \frac{\partial^{2} ψ}{\partial y^{2}} + \frac{\partial^{2} ψ}{\partial z^{2}} + \frac{8 π^{2} m}{h^{2}} (E - V) ψ = 0

None of the above.

Wave mechanical model of the atom depends upon

De-Broglie concept of dual nature of electron
Heisenberg uncertainty principle
Schrodinger uncertainty principle
All

$ψ^{2} (r, θ, ϕ)$ represents: (for Schrodinger wave mechanical model)

Amplitude of electron wave
Probability density of electron
Total probability of finding electron around nucleus
Orbit

Radial amplitude of electron wave can be represented by

R (r)

R^{2} (r)

4 {πr}^{2}

4 {πr}^{2} R^{2} (r)

The Schrodinger wave equation for hydrogen atom is $ψ (radial) = \frac{1}{16 \sqrt{4}} {(\frac{Z}{a_{0}})}^{3 / 2} [(σ - 1) (σ^{2} - 8 σ + 12)] e^{- σ / 2}$ where $a_{0}$ and Z are the constant in which answer can be expressed and $σ = \frac{2 Zr}{a_{0}}$ minimum and maximum position of radial nodes from nucleus are ........ respectively.

\frac{a_{0}}{Z}, \frac{3 a_{0}}{Z}

\frac{a_{0}}{2 Z}, \frac{a_{0}}{Z}

\frac{a_{0}}{2 Z}, \frac{3 a_{0}}{Z}

\frac{a_{0}}{2 Z}, \frac{4 a_{0}}{Z}

Which of the following pair is isodiaphers?

{}_{6}^{14}C and {}_{11}^{23}{Na}

{}_{12}^{24}{Mg} and {}_{11}^{23}{Na}

{}_{2}^{4}{He} and {}_{8}^{16}O

{}_{6}^{12}C and {}_{7}^{15}N

Which of the following does not characterise X-rays?

The radiation can ionise the gas
It causes fluorescence effect on ZnS
Deflected by electric and magnetic fields
Have wavelength shorter than ultraviolet rays

The correct expression derived for the energy of an electron in the n^th energy level is for H-atom

E_{n} = \frac{2 π^{2} {me}^{4} K^{2}}{n^{2} h^{2}}

E_{n} = - \frac{π^{2} {me}^{4} K^{2}}{2 n^{2} h^{2}}

E_{n} = - \frac{2 π^{2} {me}^{2} K^{2}}{n^{2} h^{2}}

E_{n} = - \frac{2 π^{2} {me}^{4} K^{2}}{n^{2} h^{2}}

For any H like system, the ratio of velocities of I, II & III orbit i.e., $V_{1} : V_{2} : V_{3}$ will be

1 : 2 : 3
1 : 1/2 : 1/3
3 : 2 : 1
1 : 1 : 1

Number of waves produced by an electron in one complete revolution in n^th orbit is:

n

n^{2}

(n + 1)

(2 n + 1)

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