Which among the following electron transitions $(n_2 \rightarrow n_1)$ in a $H$-atom results in the minimum change in its orbit radius $(r_2 - r_1)$?

Explain: "Rutherford's atomic model cannot explain the stability of an atom."

If the wave number of radiation emitted for the electron transition from an excited state to ground state of hydrogen is $\frac{5x}{36} \ m^{-1}$,the wave number of radiation absorbed for the electron transition from the above excited state to the next immediate excited state in $m^{-1}$ is:

Match the following for hydrogen atom $(Z=1)$ :-

$(P). \lambda_{\max }$ in Lyman series	$(i). \infty \rightarrow 1$
$(Q). v_{\min }$ in Balmer series	$(ii). 2 \rightarrow 1$
$(R). \lambda_{\min }$ in Lyman series	$(iii). 3 \rightarrow 2$
$(S). v_{\max }$ in Balmer series	$(iv). \infty \rightarrow 2$

The angular momentum of an electron in a stationary state of $Li^{2+} (Z=3)$ is $\frac{3h}{\pi}$. The radius and energy of that stationary state are respectively:

The number of maximum possible different spectral lines obtained in the Balmer series,when an electron makes a transition to the ground state from the $5^{th}$ excited state in a sample of hydrogen atoms,is: