• 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^2a_0/Z (radius shrinks with Z), v_n = Zv_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.