(a)Find the wavelength of the radiation required to excited the electron is `Li^(++)` from the first to the third Bohr orbit (b) How many spectral lines are obseved in the emission spactrum 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.