If the shortest wavelength of the Lyman series of the $H$ atom is $x$,then calculate the total energy of the $H$ atom in the first excited state.

Which hydrogen-like species will have the same radius as that of the $1^{st}$ Bohr orbit of a hydrogen atom?

The energy associated with the electron in the first orbit of a hydrogen atom is $-2.18 \times 10^{-18} \ J$. The frequency of the light required (in $Hz$) to excite the electron to the fifth orbit is $(h = 6.6 \times 10^{-34} \ Js)$

The ratio of velocity of electron in the second orbit of $He^{+}$ to the third orbit of $B^{4+}$ is $:-$

The work functions of two metals ($M_A$ and $M_B$) are in the $1:2$ ratio. When these metals are exposed to photons of energy $6 \ eV$, the kinetic energy of liberated electrons of $M_A:M_B$ is in the ratio of $2.642:1$. The work functions (in $eV$) of $M_A$ and $M_B$ are respectively.

The values of Planck's constant and the speed of light are $6.63 \times 10^{-34} \ J \ s$ and $3.0 \times 10^8 \ m \ s^{-1}$ respectively. Find the approximate wavelength in nanometers $(nm)$ of a light ray with a frequency of $8 \times 10^{15} \ s^{-1}$.