Given below are two statements :
Statement I : Rutherford's gold foil experiment cannot explain the line spectrum of hydrogen atom.

Statement II : Bohr's model of hydrogen atom contradicts Heisenberg's uncertainty principle.

In the light of the above statements, choose the most appropriate answer from the options given below:

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal to $\frac{{\mathrm{h}}^2}{\mathrm{x} {\mathrm{ma}}_0^2}.$ The value of $10 \mathrm{x}$ is (${\mathrm{a}}_0$ is radius of Bohr's orbit)

(Nearest integer)

[Given: $\pi =3.14$]

A ball weighing $10 \mathrm{g}$ is moving with a velocity of $90 \mathrm{m} {\mathrm{s}}^{-1}.$ If the uncertainty in its velocity is $5\%$, then the uncertainty in its position is _  $\times {10}^{-33} \mathrm{m}.$ (Rounded off to the nearest integer)

[Given: $\mathrm{h}=6.63\times {10}^{-34} \mathrm{Js}$]

Given below are two statements :
Statement I : According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in positive charges on the nucleus as there is no strong hold on the electron by the nucleus.
Statement II : According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in principle quantum number.

In the light of the above statements, choose the most appropriate answer from the options given below:

An accelerated electron has a speed of $5\times {10}^6{ \mathrm{ms}}^{-1}$ with an uncertainty of $0.02\%$. The uncertainty in finding its location while in motion is $x\times {10}^{-9} \mathrm{m}$.
The value of $x$ is __________. (Nearest integer)

[Use mass of electron$=9.1\times {10}^{-31} \mathrm{kg}$,

$\left.\mathrm{h}=6.63\times {10}^{-34}\mathrm{Js},\mathrm{\pi }=3.14\right]$

A source of monochromatic radiation wavelength $400 \mathrm{nm}$ provides $1000 \mathrm{J}$ of energy in $10$ seconds. When this radiation falls on the surface of sodium, $\mathrm{x}\times {10}^{20}$ electrons are ejected per second. Assume that wavelength $400 \mathrm{nm}$ is sufficient for ejection of electron from the surface of sodium metal. The value of $\mathrm{x}$ is ______. (Nearest integer)

$\left(\mathrm{h}=6.626\times {10}^{-34} \mathrm{Js}\right)$