Question

A double ionized lithium atom is hydrogen-like with atomic number $3$.
(a) Find the wavelength of the radiation required to excite the electron in $Li++$ from the first to the third Bohr orbit. (Ionization energy of the hydrogen atom equals $13.6eV$)\
(b) How many spectral lines are observed in the emission spectrum of the above excited system?

• A. $114.7A^{\circ }$, Three lines.
• B. $113.7A^{\circ }$, four lines.
• C. $115.7A^{\circ }$, two lines.
• D. $116.7A^{\circ }$, one lines.

Answer 1

The correct option is B $113.7A^{\circ }$, four lines.

formula used $=-13.6\frac{z^2}{n^2}eV$

now, for $n=1,E_i=-122.4eV$

for $n=3,E_j=-13.6eV$

now, photon energy required $E_p=E_j-E_i$

$\frac{ho}{\lambda }=\{-13.6-(-122.4\left)\right\}eV$

$\lambda =\frac{12400eV}{108.8eV}-A$

$\lambda =113.97A$

spectral lines are $3\to 2\to 1\to 0$

$\therefore$ four lines

$\therefore$ Option $\left(B\right)113.7A^o$, four lines is correct option