A hydrogen like atom (described by the Bohr model) is observed ot emit ten wavelengths, originating from all possible transition between a group of levels. These levels have energies between - 0.85 eV and -0.544 eV (including both these values). (a) Find the atomic number of the atom.
(b) Calculate the smallest wavelength emitted in these transitions. (Take ground state energy of hydrogen atom =- 13.6 eV)

Answer

A, B, D

Explanation

(a) Let these two levels are `n_1 and n_2.` Then,
`-0.85 =- (13.6(Z))^2/(n_1^2) ….(i)`
`0.544 = -(13.6(Z))^2/(n_2^2) ….(ii)`
Total number of line between `n_2 and n_1` are
given by
`((n_2 - n_1)/(n_2 - n_1 +1))/(2) = 10 ….(iii)`
Solving these equation, we get
`Z =4, n_1 = 16 and n_2 = 20`
(b) Smallest wavelength means maximum energy.
`DeltaE_(max) = E_(n_2) - E_(n_1) = - 0.544 +0.85`
= 0.306 eV
`lambda_(min) = (12375)/(0.306) = 40441 Å.`