From the above equations, it is evident that the value of energy becomes more negative and that of radius becomes smaller with increase of Z . This means that electron will be tightly bound to the nucleus. e) It is also possible to calculate the velocities of electrons moving in these orbits. Although the precise equation is not given here, qualitatively the magnitude of velocity of electron increases with increase of positive charge on the nucleus and decreases with increase of principal quantum number.
. . Explanation of Line Spectrum of Hydrogen Line spectrum observed in case of hydrogen atom, as mentioned in section . .
, can be explained quantitatively using Bohr’s model. According to assumption , radiation (energy) is absorbed if the electron moves from the orbit of smaller Principal quantum number to the orbit of higher Principal quantum number, whereas the radiation (energy) is emitted if the electron moves from higher orbit to lower orbit. The energy gap between the two orbits is given by equation ( . ) ∆ E = E f – E i ( .
) Combining equations ( . ) and ( . ) E R R H f H i (where n i and n f stand for initial orbit and final orbits) ∆ E R J H i f i f . ( .
) The frequency ( ν ) associated with the absorption and emission of the photon can be evaluated by using equation ( . ) . . J Js i f ( .
) . i f Hz ( . ) and in terms of wavenumbers ( ) ( . ) = .
s m s s i f = 09677 . i f m ( . ) In case of absorption spectrum, n f > n i