The shortest wavelength in the Balmer series of hydrogen atom is equal to the shortest wavelength in the Brackett series of a hydrogen like atom of atomic number z . The value of z is

Step-by-step solution

Using Rydberg's formula, 1 =R_H Z^2 [ 1 n ^2 - 1 ~m ^2 ] where R_H is the Rydberg's constant For calculating the shortest wavelength in the Balmer series of hydrogen atom, aligned & n =2, ~m = and Z =1 & ₁= 4 R _ H aligned For hydrogen like atom, the shortest wavelength is given by, In Brackett series array ll & n =4, ~m = & 1 ₂ = R _ H Z ^2 ( 1 16 ) & ₂= 16 R _ H Z ^2 & Given: ₁= ₂, & 4 R _ H = 16 R _ H Z ^2 Z ^2=4 & Z =2 array