If the first excitation potential of a hypothetical hydrogen like atom is (15 ~V ), then the third excitation potential of the atom is

Step-by-step solution

Let total energy of hydrogen like atom at ground state (=-E ) So, Ist excitation ( aligned Energy & =E_ 2 n d -E_ 1 s t 15 eV & = ( -E 2^2 )- [ E 1^2 ] aligned ) ( ( ) First excitation potential is given) ( array ll & 3 E 4 =15 eV & E= 15 4 3 eV =20 eV array ) Now, the third excitation energy ( aligned E₃ & =E_ 4^ th -E_ 1^ st & = ( -E 4^2 )- [ E 1^2 ] E₃ & =+ 15 E 16 aligned ) Now, putting the value of (E ), we get (E₃= 15 16 20= 75 4 eV ) Hence, the correct option is (d).