• $summary_{type}$: application
• $word_{count}$: 170

Hydrogen-like ions (He+, Li2+, Be3+) have one electron and nuclear charge Z. All Bohr formulas apply with Z scaling: $r_n$ = $n^2$$a_0$/Z (radius shrinks with Z), $v_n$ = Z$v_0$/n (speed increases with Z), $E_n$ = -13.6*$Z^2$/$n^2$ eV (binding strengthens as $Z^2$). For He+ (Z=2): ground state energy = -54.4 eV, ionization energy = 54.4 eV. For Li2+ (Z=3): ground state energy = -122.4 eV. Spectral wavelengths scale as 1/$Z^2$ — all lines shift to shorter wavelengths for higher Z. A powerful JEE concept: certain transitions in different ions produce the same wavelength. For example, the 2 to 1 transition in He+ (Z=2) has 4 times the energy of 2 to 1 in H, giving lambda/4. The n=2 to n=1 transition in He+ has the same energy as n=4 to n=2 in H (both give 1/lambda = 3R). JEE frequently asks to match overlapping spectral lines between hydrogen and hydrogen-like ions.