The shortest wavelength of the Brackett series of a hydrogen like atom of atomic number Z is same as the shortest wavelength of the Balmer series of hydrogen atom, then the value of Z is –
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(2)
Shortest wavelength of Brackett series corresponds to the transition of electron between
and
and the shortest wavelength of Balmer series corresponds to the transition of electron between
and 
So,
or
or
or 
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