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 the following relation: 
1. $2\mathrm{\pi r}=\mathrm{n\lambda }$
2. $\mathrm{\pi r}$ $=$ $2\mathrm{n\lambda }$
3. $\mathrm{mvr}$ $=$ $\mathrm{n\lambda }$
4. $\mathrm{vr}$ $=$ $2\mathrm{n\lambda }$

Which among the following are isoelectronic species?

1. ${\mathrm{Na}}^{+},<mspace\; width="1em"></mspace>{\mathrm{K}}^{+},<mspace\; width="1em"></mspace>{\mathrm{Ca}}^{2+},<mspace\; width="1em"></mspace>{\mathrm{Mg}}^{2+}$

2. ${\mathrm{Ca}}^{2+},<mspace\; width="1em"></mspace>{\mathrm{Mg}}^{2+},<mspace\; width="1em"></mspace>{\mathrm{S}}^{2-},<mspace\; width="1em"></mspace>{\mathrm{K}}^{+}$

3. ${\mathrm{Ca}}^{2+},<mspace\; width="1em"></mspace>\mathrm{Ar},<mspace\; width="1em"></mspace>{\mathrm{S}}^{2-},<mspace\; width="1em"></mspace>{\mathrm{K}}^{+}$

4. None of the above

Find the total number of photons emitted by neon gas if the radiation has a wavelength of 616 nm and a total energy of 2 J.
1. \(6.2 \times 10^{-18} \)
2. \(5.6 \times 10^{17} \)
3. \(6.2 \times 10^{18} \)
4. \(32.2 \times 10^{-20}\)

Which of the following gives the atomic numbers of the elements having outermost electronic configurations 3s¹ and 2p⁵, respectively?

The number of electrons that can be present in the subshells having m_s value of \(-\frac{1}{2}\) for n = 4 are:

Identify the element with the highest number of unpaired electrons in its ground state from the given options :

The unpaired electrons in aluminium and silicon occupy 3p orbitals in their ground states. Which of the following experiences a greater effective nuclear charge?

1. Electrons in the 3p orbital of silicon

2. Electrons in the 5d orbital of aluminium

3. Electrons in the 3p orbital of aluminium

4. Both experience the same effective nuclear charge

 

If the position of the electron were measured with an accuracy of +0.002 nm, the uncertainty in the momentum of the electron would be: 

1. 5.637 × 10^–23 kg m s^–1

2. 4.637 × 10^–23 kg m s^–1

3. 2.637 × 10^–23 kg m s^–1

4. 3.637 × 10^–23 kg m s^–1

1. 32.22 × 10^–16 J

2. 12.22 × 10^–16 J

3. 22.27 × 10^–16 J

4. 31.22 × 10^–16 J