If ${\mathrm{\lambda }}_0$ and $\mathrm{\lambda }$ be the threshold wavelength and the wavelength of incident light, the velocity of photo-electrons ejected from the metal surface is:

1.  $\sqrt{\frac{2\mathrm{h}}{\mathrm{m}}\left({\mathrm{\lambda }}_0-\mathrm{\lambda }\right)}$

2.  $\sqrt{\frac{2\mathrm{hc}}{\mathrm{m}}\left({\mathrm{\lambda }}_0-\mathrm{\lambda }\right)}$

3.  $\sqrt{\frac{2\mathrm{hc}}{\mathrm{m}}\left(\frac{{\mathrm{\lambda }}_0-\mathrm{\lambda }}{{\mathrm{\lambda \lambda }}_0}\right)}$

4.  $\sqrt{\frac{2\mathrm{h}}{\mathrm{m}}\left(\frac{1}{{\mathrm{\lambda }}_0}-\frac{1}{\lambda }\right)}$

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

 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

 $\sqrt{\mathrm{V}}$on two particles A and B are plotted against de-Broglie wavelengths. Where V is the potential on the particles. Which of the following relation is correct about the mass of particles?

1.  ${\mathrm{m}}_{\mathrm{A}}={\mathrm{m}}_{\mathrm{B}}$

2.  ${\mathrm{m}}_{\mathrm{A}}>{\mathrm{m}}_{\mathrm{B}}$

3.  ${\mathrm{m}}_{\mathrm{A}}<{\mathrm{m}}_{\mathrm{B}}$

4.  ${\mathrm{m}}_{\mathrm{A}}\le {\mathrm{m}}_{\mathrm{B}}$

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

1.		2.
3.		4.

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

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

Given below are two statements:

Statement 1: The ground state electronic configuration of nitrogen is

Statement 2: Electrons are filled in orbitals as per the Aufbau principle, Hund's rule of maximum spin multiplicity, and Pauli's principle.

1.  If both the statement are true and statement -2 is the correct explanation of statement-1

2.  If both the statements are true but statement-2 is not the correct explanation of statement-1

3.  If statement-1 is true and statement-2 is false

4.  If statement-1 is false and statement-2 is true