Question

A hydrogen like atom in ground state absorbs 'n' photons having the same energy and it emits exactly 'n' photons when electronic transition takes place. Then the energy of the absorbed photon may be
a)91.8 eV
b)40.8 eV
c)48.4 eV
d)54.4 eV

Answer 1

answer : options (a) and (b)

explanation : since, it is given that A hydrogen like atom in ground state absorbs n photons having the same energy and it emits exactly n photons when electronic transition takes place.

therefore, transition must have taken place from 1 to 2.

from formula,

E = 13.6Z² [ 1/1² - 1/2²]

= 13.6 Z² [ 1 - 1/4 ]

= 13.6 Z² × 3/4

= 10.2 Z² eV

if we put Z = 2,

then, E = 10.2 × 2² = 40.8 eV hence, option (b) is correct

and if we put Z = 3

then, E = 10.2 × 3² = 91.8 eV hence, option (a) is correct.