The energy required to dislodge an electron from an excited isolated $H^-$ ion,given that the ionization energy of a ground state $H$ atom is $IE_1 = 13.6 \ eV$,is:

Observe the following statements:
Statement-$I$: Rutherford model of an atom cannot explain the stability of an atom.
Statement-$II$: The wavelength of $X$-rays is higher than the wavelength of microwaves.
The correct answer is:

The ratio of the radius of the $2^{nd}$ orbit of $H$ to the radius of the $3^{rd}$ orbit of $He^{+}$ is ......

State whether the following statements are true or false:
$(i)$ In Rutherford's atomic model,the Coulombic forces between the nucleus and electrons are mathematically similar to the gravitational forces $F = G \frac{m_1 m_2}{r^2}$.
$(ii)$ Out of every $20000$ $\alpha$-particles,$\sim 10$ particles bounce back after hitting the gold foil.
$(iii)$ In Rutherford's experiment,a zinc sulfide $(ZnS)$ fluorescent screen is placed around the gold foil.
$(iv)$ Rutherford's $\alpha$-particle scattering experiment is related to the size of the atomic nucleus.

Calculate the energy associated with the first orbit of $He^{+}$. What is the radius of this orbit?

The energy of an electron in the first Bohr orbit of hydrogen atom is $-2.18 \times 10^{-18} \ J$. Its energy in the third Bohr orbit is $........$.