The wavenumber of first spectral line of Lyman series of $\mathrm{He}^{+}$ion is $x \mathrm{~m}^{-1}$. What is the wave number ( $\mathrm{in}^{-1}$ ) of second spectral line of Balmer series of $\mathrm{Li}^{2+}$ ion?

The uncertainty in determination of position of a small ball of mass 10 g is $10^{-33} \mathrm{~m}$. With what $\%$ of accuracy its speed can be measured, if it has a speed of 52.5 $\mathrm{ms}^{-1} ?\left(h=6.6 \times 10^{-34} \mathrm{Js}\right)$

The kinetic energy of electrons emitted, when radiation of frequency $1.0 \times 10^{15} \mathrm{~Hz}$ hits a metal, is $2 \times 10^{-19} \mathrm{~J}$. What is the threshold frequency of the metal (in Hz )? $\left(h=6.6 \times 10^{-34} \mathrm{Js}\right)$

Identify the pair of species having same energy from the following. (The number given in the bracket corresponds to principal quantum number ( $n$ ) in which the electron is present.)