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Question:

When an electron in a hydrogen atom jumps from the excited state to the ground state, how would the de Broglie wavelength associated with the electron change?

Solution:

Kinetic energy of an electron in an orbit in Bohr's model for a Hydrogen atom is given by: E = 13.6/n² eV

de Broglie wavelength of an electron is given by:
λ = h/p

But, p = √(2mE)

λ = h/√(2mE) => λ ∝ 1/√E

Hence, when an electron jumps from the excited state to the ground state, its kinetic energy (E) increases, and therefore its de Broglie wavelength (λ) decreases.