The ratio between the radii of $He^{+}$ ion and $H$ atom is:

The energy of an electron in the first Bohr orbit of $H$-atom is $-13.6 \ eV$. The possible energy value of an electron in the first excited state of $Li^{2+}$ is (in $eV$)

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.

When an electron jumps from $L$ to $K$ shell,what happens to the energy?

Supposing the energy of the fourth shell for a hydrogen atom is $-25 \, a.u.$ (arbitrary unit). What would be its potential energy in the ground state?

$A$ $124 \ W$ bulb converts only $15 \ \%$ of the energy supplied to it into visible light of wavelength $640 \ \text{nm}$. How many photons are emitted by the light bulb in one second?