Determine the de Broglie wavelength of the photoelectron emitted when a photon,
produced by the de-excitation of a He⁺ ion with an electron having
a de Broglie wavelength of 3.329 Å, ionizes a hydrogen atom in its ground state.

1. 0.1518 Å

2. 6.1518 Å

3. 2.3518 Å

4. 4.1218 Å

Calculate the de Broglie wavelength of an $\alpha$-particle emitted from radium having an energy of 4.8 MeV.

(Given: Mass of $\alpha$-particle=6.6 x 10^-24 g; h=Planck's constant = 6.626 x 10^-27 erg sec)

1. 6.18 x 10^-13 cm

2. 0.58 x 10^-8 cm

3. 6.58 x 10^-13 cm

4. 4.12 x 10^-11 cm

What is the ratio of the time period of revolution of electron He⁺ ion sample in the orbit where the path length is three time the de-broglies wavelength to the time period of revolution in the ground state –

1. 27:1

2. 1:27

3. 9:8

4. 8:9

For particles with equal kinetic energy, how is the de Broglie wavelength related to:

1. Directly proportional to its velocity

2. Inversely proportional to its velocity

3. Independent of velocity and mass

4. Unpredictable

An electron, practically at rest, is initially accelerated through a potential difference of 100 volts. It then has a de Broglie wavelength=$\lambda$₁Å. It then get retarded through 19 volts and then it has wavelength $\lambda$₂ Å. A further retardation through 32 volts changes the wavelength to $\lambda$₃.

What is ($\lambda$₃-$\lambda$₂)/$\lambda$₁?

1. 20/41

2. 10/63

3. 20/63

4. 10/41

A cricket ball of 0.5 kg is moving with a velocity of 100 ms^-1. The wavelength associated with its motion is:

1. 1/100cm

2. 6.6 x 10^-34m

3. 1.32 x 10^-35m

4. 6.6 x 10^-28m

If the velocity of a particle is reduced to 1/3^rd, then percentage increase in its de-broglie wavelength will be:-

1. 100%

2. 200%

3. 50%

4. 33.33%

 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.