When the electron orbiting in hydrogen atom goes from one orbit to another orbit (principal quantum number =n ), the de-Broglie wavelength ( ) associated with it is related to n as

Step-by-step solution

The relationship between the de Broglie wavelength and principal quantum number n for an electron in a hydrogen atom follows from Bohr's quantization condition and the de Broglie hypothesis. The angular momentum quantization requires mvr = n h 2 , where m denotes electron mass, v orbital velocity, r orbital radius, and h Planck's constant. The de Broglie wavelength is given by = h mv . Substituting mv = nh 2 r from the quantization condition yields = 2 r n , establishing r n . Since the Bohr radius scales as r_n =