Question

In the Bohr model of the hydrogen atom, the allowed orbits of the electron (labeled n = 1, 2, 3, …) have angular momentum , orbital radii , and energies . In these expressions me is the mass of the electron.

(a) Rank the first three allowed orbits of the hydrogen atom, n = 1, n = 2, and n = 3, in order of the energy of the electron, from highest to lowest energy. (Note that since the energies are negative, “highest” means “least negative” and “lowest” means “most negative.”) If any two orbits have the same energy, state this. Explain how you made your ranking.

(b) Rank the first three allowed orbits of the hydrogen atom, n = 1, n = 2, and n = 3, in order of the orbital speed of the electron, from fastest to slowest. If any two orbits have the same orbital speed, state this. Explain how you made your ranking.

Answer 1

First three Bohr orbits of hydrogen are to be arranged in order of decreasing 1) energy of electron 2) decreasing speed of electron

(a) In hydrogen atom , energy of nth orbit 12 - 13.6ev But En being n increases I Enl decreases positive it increases as n increases. So, first 3 carbits in Blohn hydrogen atom when ranked from highest to lowest are energy 123 orbit > nz2 arbit > nal orbit (Answer) th In be the orbital speed inn arbit, (2) ff me un atto in rm me un? 4TTE Nn In 4 IT tome in e and hence As n rn VATTE mern ind una increases increases un decreases & order of 1st 3 orbits in slowest electronic motion fastest to is nal orbit >n22 orbit > nz3 orbit (Auswen)