A proton and an alpha particle are accelerated in a field of the same potential difference. Then, the ration of the Brigle wavelengths associated with the moving material particles is:

Experimentally it is found that $12.8 \mathrm{eV}$ energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is $\frac{9}{x}\times {10}^{-10} \mathrm{m}$.

The value of the $x$ is: _____.

($1 \mathrm{eV}=1.6\times {10}^{-19} \mathrm{J}, \frac{1}{4\pi {\epsilon }_0}=9\times {10}^9 \frac{{\mathrm{Nm}}^2}{{\mathrm{C}}^2}$ and electronic charge $=1.6\times {10}^{-19} \mathrm{C}$)

A beam of fast moving alpha particles were directed towards a thin film of Gold. The parts $A^{\text{'}}, B^{\text{'}}$ and $C^{\text{'}}$ of the transmitted and reflected beams corresponding to the incident parts $A, B$ and $C$ of the beam are shown in the adjoing diagram. The number of alpha particles in

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$