$A$ $25 \ W$ bulb emits monochromatic yellow light of wavelength $0.57 \ \mu m$. Calculate the rate of emission of quanta per second.

One energy difference between the states $n = 2$ and $n = 3$ is $E \ eV$,in a hydrogen atom. The ionization potential of the $H$ atom is ............. $E$.

If the series limit of wavelength of the Lyman series for the hydrogen atom is $912 \ \mathring{A}$,then the series limit of wavelength for the Balmer series of radiation which may be emitted is :

Which of the following statements is incorrect?

The energy of an electron in an orbit of a hydrogen-like ion with an orbit radius of $52.9 \ pm$ in $J$ is (ground state energy of an electron in a hydrogen atom is $-2.18 \times 10^{-18} \ J$).

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.