$A$ single-electron species has a nuclear charge of $+Ze$,where $Z$ is a constant. The energy required to excite an electron from the $2^{nd}$ Bohr orbit to the $3^{rd}$ Bohr orbit is $47.2 \ eV$. Calculate the value of $Z$.

When a hydrogen atom in an excited state undergoes electronic transitions to the ground state,$5$ spectral lines are observed in the ultraviolet region. How many spectral lines will be observed in the infrared region due to transitions from the same excited state?

$A$ bulb is rated at $150 \text{ W}$,converting $8\%$ of its energy into light. If the energy of one photon is $4.42 \times 10^{-19} \text{ J}$,how many photons are emitted by the bulb per second?

Explain the following according to Bohr's model of hydrogen:
$(i)$ Principal quantum number
$(ii)$ Radius of stationary orbit $(r)$
$(iii)$ Energy of stationary state
$(iv)$ Isoelectronic ion of $H$
$(v)$ Velocity of electron

Number of waves made by Bohr's electron in one complete revolution in the $3^{rd}$ orbit.

Rutherford's $\alpha$-particle scattering experiment eventually led to the conclusion that