The circumference of the Bohr orbit for the H atom is related to the de Broglie wavelength associated with the electron revolving around the orbit by which of the following relation?

$1. 2\mathrm{\pi r}=\mathrm{n\lambda }$
2. πr = 2nλ
3. mvr = nλ
4. vr = 2nλ

 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 wavelength of an electron moving with a velocity of 2.05 × 10⁷ m s^-1  would be 

$1. 4.65 \times {10}^{-12 }\mathrm{m}$
2. 3.55 × 10^-11 m
3. 2.34 × 10¹¹ m
4. 6.43 × 10^-11 m

If the velocity of the electron is 1.6 × 10⁶ ${\mathrm{ms}}^{-1}$. The de Broglie wavelength associated with this electron is 

$$\begin{gathered} 1. 590 \mathrm{pm} \\ 2. 455 \mathrm{pm} \\ 3. 512 \mathrm{pm} \\ 4. 401 \mathrm{pm} \end{gathered}$$

The graphs that represents the variation of momentum of particle with de-Broglie wavelength is 

1.  

2.  

3.  

4.  

Which of the following statements is wrong?

1. The uncertainty principle is $∆x·∆p\ge \frac{h}{4\mathrm{\pi }}$

2. Half-filled and fully filled orbitals have greater stability due to greater exchange energy,

greater symmetry, and a more balanced arrangement.

3. The energy of the 2s orbital is less than the energy of the 2p orbital in the case of hydrogen-like atoms.

4. De-Broglie's wavelength is given by $\lambda =\frac{h}{mv}$, where m= mass of the particle, v = group velocity of the particle.

The velocity associated with a proton moving at a potential difference of 1000 V is 4.37 × 10⁵ ms^–1. If the hockey ball of mass 0.1 kg is moving with this velocity, then the wavelength associated with this velocity would be

$$\begin{gathered} 1. 1.52 \times {10}^{-38} \mathrm{m} \\ 2. 2.54 \times {10}^{-32} \mathrm{m} \\ 3. 1.52 \times {10}^{-36} \mathrm{m} \\ 4. 3.19 \times {10}^{-34} \mathrm{m} \end{gathered}$$

The kinetic energy of an electron is 3.0 × 10^–25 J. Its wave length would be 

1. 8.96 × 10^-7 m
2. 4.37 × 10^-6 m
3. 1.32 × 10^-7 m
4. 2.89 × 10^-4 m

If the wavelength of a neutron is 800 pm, then the characteristic velocity associated with the neutron is

1. 494 m s^-1
2. 567 m s^-1
3. 494 cm s^-1
4. 501 m s^-1