The radius of the first Bohr orbit for hydrogen is $0.53 \ \mathring{A}$. The radius of the third Bohr orbit would be .............. $\mathring{A}$.

The binding energy of an $e^-$ in the ground state of a hydrogen atom is $13.6 \ eV$. The energy required to remove an electron from the ground state of a $He^+$ ion is:

The energy required (in $eV$) to excite an electron of $H$-atom from the ground state to the third excited state is

The wavelength of the first line of the Balmer series is $656 \ nm$. Calculate the wavelength of the second line of this series. (Note: First line means $n=3 \to n=2$ and second line means $n=4 \to n=2$)

$A$ source of monochromatic radiation of wavelength $400 \, nm$ provides $1000 \, J$ of energy in $10 \, seconds$. When this radiation falls on the surface of sodium,$x \times 10^{20}$ electrons are ejected per second. Assume that wavelength $400 \, nm$ is sufficient for ejection of electrons from the surface of sodium metal. The value of $x$ is $......$. (Nearest integer) $(h = 6.626 \times 10^{-34} \, Js)$

The wavenumber of the first line $(n_2=3)$ in the Balmer series of hydrogen is $\bar{\nu}_1 \ cm^{-1}$. What is the wavenumber (in $cm^{-1}$) of the second line $(n_2=4)$ in the Balmer series of $He^{+}$?