The number of unpaired electrons in 1s² 2s² 2p³ is -

1. 2

2. 0

3. 3

4. 1

${\mathrm{Be}}^{3+}$ion and a proton are accelerated by the same potential. The ratio of their de-Broglie wavelengths is

(assume mass of proton =  mass of neutron)

1. 1:2

2. 1:4

3. 1:1

4. 1:$3\sqrt{3}$

The incorrect statement about the nodal plane among the following is: 

The quantum number not obtained from Schrodinger’s wave equation is:

A dye absorbs a photon of wavelength $\mathrm{\lambda }$ and re-emits the same energy into two photons of wavelengths ${\mathrm{\lambda }}_1$ $$ and ${\mathrm{\lambda }}_2$ respectively. The wavelength $\mathrm{\lambda }$ is related to ${\mathrm{\lambda }}_1$ and ${\mathrm{\lambda }}_2$ as:

1.  $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_1+{\mathrm{\lambda }}_2}{{\mathrm{\lambda }}_1{\mathrm{\lambda }}_2}$

2.  $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_1{\mathrm{\lambda }}_2}{{\mathrm{\lambda }}_1+{\mathrm{\lambda }}_2}$

3.  $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_1^2+{\mathrm{\lambda }}_2^2}{{\mathrm{\lambda }}_1+{\mathrm{\lambda }}_2}$

4.  $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_1{\mathrm{\lambda }}_2}{{\left({\mathrm{\lambda }}_1+{\mathrm{\lambda }}_2\right)}^2}$

The excited state of an H atom emits a photon of wavelength $\mathrm{\lambda }$ and returns to the ground state. The principal quantum number of the excited state is given by:

1.  $\sqrt{\mathrm{\lambda R}\left(\mathrm{\lambda R}-1\right)}$

2.  $\sqrt{\frac{\mathrm{\lambda R}}{\left(\mathrm{\lambda R}-1\right)}}$

3.  $\sqrt{\mathrm{\lambda R}\left(\mathrm{\lambda R}+1\right)}$

4.  $\sqrt{\frac{\left(\mathrm{\lambda R}-1\right)}{\mathrm{\lambda R}}}$

Identify the graph that correctly depicts the variation of momentum with the de-Broglie wavelength of a particle. 

1.		2.
3.		4.

 The largest de Broglie wavelength among the following (all have equal velocity) is: 

1.  ${\mathrm{CO}}_2$ molecule

2.  ${\mathrm{NH}}_3$ molecule

3.  Electron

4.  Proton

The ratio of slopes of ${\mathrm{K}}_{\max } \mathrm{vs}. \mathrm{v} \mathrm{and} {\mathrm{V}}_0 \mathrm{vs}. \mathrm{v}$ curves in photoelectric effect gives -

(v=frequency, ${\mathrm{K}}_{\max }$=maximum kinetic energy, ${\mathrm{V}}_0$ stopping potential):

1.  Charge of electron

2.  Planck's constant

3.  Work function

4.  The ratio of Planck's constant of electronic charge