If the diameter of a carbon atom is 0.15 nm, the number of carbon atoms that can be placed side by side in a straight line across the length of the scale of length 20 cm long will be:$\mathrm{}$

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 energy of an electron in the first Bohr's orbit of an H-atom is -13.6 eV. The possible energy value (s) of the excited state(s) for electrons in Bohr's orbits of hydrogen is (are):

1. -3.4 eV

2. -4.2 eV

3. -6.8 eV

4. +6.8 eV

For any H-like system, the ratio of velocities of I, II & III orbit i.e., ${\mathrm{V}}_1<mspace\; width="1em"></mspace>:<mspace\; width="1em"></mspace>{\mathrm{V}}_2<mspace\; width="1em"></mspace>:<mspace\; width="1em"></mspace>{\mathrm{V}}_3$ will be:

1.  1 : 2 : 3

2.  1 : 1/2 : 1/3

3.  3 : 2 : 1

4.  1 : 1 : 1

The concept that contradicts the Bohr Model of an atom is: 

Which of the following ions has the same radius as the first Bohr orbit of the hydrogen atom?

1. ${\mathrm{He}}^{+},$ $n=2$

2. ${\mathrm{Li}}^{2+},n=2$

3. ${\mathrm{Be}}^{3+},$ $n=2$

4. ${\mathrm{Li}}^{2+},\mathrm{n}=3$

If the size of the first orbit of the hydrogen atom is 5.29 nm, the size of the second orbit of He⁺ is

1. 2.65 nm

2. 21.16 nm

3. 10.58 nm

4. 5.29 nm