Atoms Test - 11...

A diatomic molecule has moment of inertia $$I$$. By Bohrs quantization condition its rotational energy in the $$n^{th}$$ level ($$n = 0$$ is not allowed) is

In a $$\mathrm{C}\mathrm{O}$$ molecule, the distance between $$\mathrm{C}$$ (mass $$=12$$ a.m.u) and $$\mathrm{O}$$ (mass $$=16$$ a.m.u.), where 1 a.m.u $$=\displaystyle \frac{5}{3}\times 10^{-27} kg,$$ is close to 

The electrostatic energy of $$Z$$ protons uniformly distributed throughout a spherical nucleus of radius $$R$$ is given by
$$\displaystyle E=\frac { 3 }{ 5 } \frac { Z\left( Z-1 \right) { e }^{ 2 } }{ 4\pi { \varepsilon  }_{ 0 }R } $$
The measured masses of the neutron, $$\displaystyle _{ 1 }^{ 1 }{ H },\, _{ 7 }^{ 15 }{ N }$$ and $$\displaystyle _{ 8 }^{ 15 }{ O }$$ are $$1.008665\  u, 1.007825 \ u, 15.000109\  u$$ and $$15.003065\  u$$, respectively. Given that the radii of both the $$\displaystyle _{ 7 }^{ 15 }{ N }$$ and $$\displaystyle _{ 8 }^{ 15 }{ O }$$ nuclei are same, $$\displaystyle 1u=931.5\quad { MeV }/{ { c }^{ 2 } }$$ (c is the speed of light) and $$\displaystyle { { e }^{ 2 } }/{ \left( 4\pi { \varepsilon  }_{ 0 } \right)  }=1.44\,MeV\,fm$$. Assuming that the difference between the binding energies of $$\displaystyle _{ 7 }^{ 15 }{ N }$$ and $$\displaystyle _{ 8 }^{ 15 }{ O }$$ is purely due to the electrostatic energy, the radius of either of the nuclei is $$(1\, fm = 10^{-15}m)$$:

 The electric potential between a proton and an electron is given by  $$V=\displaystyle \mathrm{V}_{0}\ln\frac{\mathrm{r}}{\mathrm{r}_{0}}$$ , where $$\mathrm{r}_{0}$$ is a constant. Assuming Bohr's model to be applicable, write variation of $$\mathrm{r}_{\mathrm{n}}$$ with $$\mathrm{n},\ \mathrm{n}$$ being the principal quantum number?

For which one of the following, Bohr model is not valid?

When an $$\alpha$$-particle of mass $$'m'$$ moving with velocity $$'v'$$ bombards on a heavy nucleus of charge $$'Ze'$$, its distance of closest approach from the nucleus depends on $$m$$ as:

The energy of the em waves is of the order of 15 keV. To which part of the spectrum does it belong?

The value of Planck's constant is $$6.63\times 10^{-34}Js$$. The speed of light $$3\times 10^{17}\:nm\:s^{-1}$$. Which value is closest to the wavelength in nanometer of a quantum of light with frequency of $$6\times 10^{15}s^
{-1}$$?

The transition from the state $$n=3$$ to $$n=1$$ in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from-

Whenever a stream of electrons collides with a stream of photons, in this collision, which of the following is not conserved?