Calculate the frequency, energy and wavelength of the radiation corresponding to the spectral line of lowest frequency in Lyman series in the spectra of hydrogen atom. Also, calculate the energy for the corresponding line in the spectra of ${\mathrm{Li}}^{+2}$

$\left({\mathrm{R}}_{\mathrm{H}}=1·09678\times {10}^7 {\mathrm{m}}^{-1}, \mathrm{c}=3\times {10}^8 \mathrm{m}/\mathrm{s},Z=3, \mathrm{h}=6·625\times {10}^{-34}\mathrm{J}·\mathrm{s}\right)$

For ${\mathrm{He}}^{+}$, the energy is related to the quantum number, $\mathrm{n}$, through an expression 

${\mathrm{E}}_{\mathrm{n}}=-\frac{{\mathrm{Z}}^2\mathrm{B}}{{\mathrm{n}}^2}$,

where $\mathrm{Z}$ is the atomic number of species and $\mathrm{B}=2.179\times {10}^{-18} \mathrm{J}$.

The energy of the lowest level $\left(\mathrm{n}=1\right)$ of a ${\mathrm{He}}^{+}$ ion is $-\mathrm{x}\times {10}^{-18}\mathrm{J}$. The value of $\mathrm{x}$(the nearest integer)

Calculate the uncertainty in the velocity of an electron when the uncertainty in position is $0.1 \mathrm{nm}$.

(report your answer(up to two decimal places) in multiple of ${10}^5 \mathrm{m} {\mathrm{s}}^{-1}$)

The prominent yellow line in the spectrum of sodium vapour lamp has a wave length of $590 \mathrm{nm}$. What minimum accelerating potential is needed to excite this line in an electron tube containing sodium vapour? $\left(\mathrm{h}=6.63\times {10}^{-34} \mathrm{J}·\mathrm{s}, \mathrm{c}=3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}\right)$

Round off your answer to the nearest integer.