Question

The shortest wavelength of the Brackett series of a hydrogen like atom of atomic number Z is same as the shortest wavelength of the Balmer series of hydrogen atom, then the value of Z is ______.

Options

• 1

• 2

• 3

• 4

Answer 1

The shortest wavelength of the Brackett series of a hydrogen like atom of atomic number Z is same as the shortest wavelength of the Balmer series of hydrogen atom, then the value of Z is 2.

Explanation:

Shortest wavelength of Brackett corresponds to n = 4 and n = ∞ and shortest wavelength of Balmer series corresponds to n = 2 and n = ∞

∴ (Z²) `(13.6/16) = 13.6/4`

⇒ Z = 2