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  4. The shortest wavelength of the Brackett series of a hydrogen-like atom (atomic number =z ) is the same as the shortest wavelength of the Balmer series of hydrogen atom. The value of z is

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Q. The shortest wavelength of the Brackett series of a hydrogen-like atom (atomic number $=z$ ) is the same as the shortest wavelength of the Balmer series of hydrogen atom. The value of $z$ is

NTA AbhyasNTA Abhyas 2020

Solution:

$z^{2}\left(\frac{13 . 6}{16}\right)=\frac{13 . 6}{4}$
$\Rightarrow z^{2}=4\Rightarrow z=2$