If the shortest wavelength of the hydrogen atom in the Lyman series is $x$, then the longest wavelength in the Balmer series of $He^+$ is:

If the frequency of radiation emitted for the electron transition from an excited state to ground state of hydrogen atom is $\frac{3 X}{4} \ Hz$,the frequency of radiation absorbed for the electron transition from the above excited state to the next immediate excited state in $Hz$ is:

If the velocity of an electron in the $n^{th}$ orbit of a hydrogen atom is $0.0109 \times 10^{10} \, cm \, s^{-1}$,what is the value of $n$?

Consider one $He^{+}$ ion is in excited state $(n = 5)$. Which of the following observations hold true as per the Bohr's model?

When a metal surface is irradiated with light of frequency $x \ Hz$,the kinetic energy of emitted photoelectrons is $z \ J$. When the same metal is irradiated with light of frequency $y \ Hz$,the kinetic energy of emitted electrons is $\frac{z}{3} \ J$. What is the threshold frequency (in $Hz$) of the metal?

The ratio of the energy of a photon of $2000 \ \mathring{A}$ wavelength radiation to that of $4000 \ \mathring{A}$ radiation is