For a hydrogen atom,the energy difference between the first and second Bohr orbits is $3B/4$. What is the energy difference between the first and third Bohr orbits?

An electron initially present in an excited state of $H$ atom is further excited to another energy level by an incident photon. It releases $10$ photons while coming back to the ground state,out of which $7$ have higher energy than the incident photon. The electron was initially present in:

For the $H$ spectrum,the limiting line in the $Balmer$ series has a frequency of ...... $(R_\infty = 3.29 \times 10^{15} \text{ cycles/s})$

When $\alpha$-particles are sent through a thin metal foil,most of them go straight through the foil because (one or more are correct)

The following figure shows the spectrum of an ideal black body at four different temperatures. The number of correct statement$(s)$ from the following is $..............$.
$A$. $T_4 > T_3 > T_2 > T_1$
$B$. The black body consists of particles performing simple harmonic motion.
$C$. The peak of the spectrum shifts to shorter wavelength as temperature increases.
$D$. $\frac{T_1}{v_1} = \frac{T_2}{v_2} = \frac{T_3}{v_3} \neq \text{constant}$
$E$. The given spectrum could be explained using quantization of energy.

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: