A double ionized lithium atom is hydrogen like with atomic number `3`
(i)Find the wavelength of the radiation to excite the electron in `Li^(++)`from the first to the third bohr orbit (Ionization energy of the hydrogen atom equals `13. 6eV`
(ii) How many spectral lines are observed in the emission spectrum of the above excited system ?

Explanation

The energy of the electron in nth orbit of hydrogen-like atom is
`E_(n_ = - (Z^(2) R h c)/(n^(2))` Here , `Z = 3`
and `R h c = 13.6 e V`
a. The energy required to excite the electron in `Li^(++)` from `(n = 1)` to `(n = 3)` is
` E_(3) - E_(1) = - (Z^(2) R h c)/(3^(2)) - ((-Z^(2) R h c)/(1^(2)))`
`= Z^(2) R h c ( 1 - (1)/(9))`
`(8)/(9) = Z^(2) R h c = (8)/(9) xx (3)^(2) xx 13.6 e V`
`= 8 xx 13.6 e V = 8 xx 13.6 xx 1.6 xx 10^(-19) J`

Therefore , the wavelength of incidiation radition required for excitation is given by
`(h c)/(lambda) = E_(3) - E_(1)`
or `lambda = (h c)/(E_(3) - E_(1)) = (6.63 xx 10^(-34) xx 3 xx 10^(8))/(8 xx 13.6 xx 1.6 xx 10^(-19))`
`= 114.26 xx 10^(-10) m - 114.26 Å`
b. The possible lines in the emission spectrum of this excited system are `[(n n - 1)/(2) = 3 (3 - 1)/(2) = 3]`
Three in number , represented in figure.