Calculate the longest wavelength in the hydrogen emission spectrum of the Lyman series $\left(R_H = 109677 \ cm^{-1}\right)$.

For a $Bohr$ atom,the angular momentum of an electron is given by $M(n = 1, 2, 3, .....)$ :

The radius of the first Bohr orbit of the hydrogen atom is the same as that of the orbit $(n)$ of a hydrogen-like species $X$. The values of $(n)$ and $X$ respectively are:

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.

Calculate the wavenumber of a photon emitted during the transition from the orbit of $n=3$ to $n=2$ in a hydrogen atom. $(R_{H} = 109677 \ cm^{-1})$ (in $cm^{-1}$)

If $m$ and $e$ are the mass and charge of the revolving electron in the orbit of radius $r$ for a hydrogen atom,the total energy of the revolving electron will be: