Question #5745c
1 Answer
Explanation:
From Rutherford-Bohr's atomic model of Hydrogen we know that energy levels or velocity of an electron is defined by an positive integer
Assuming that transition here implies movement of an electron from higher to lower value of
Therefore, for an electron which can have maximum of
Similarly, for an electron which can have maximum of
One of Bohr's key hypotheses proposed was that the orbiting electron could exist only in certain special states called stationary states. In these states, the angular momentum of the electron
For a circular orbit we have momentum of an electron
From above and solving for velocity we have
Also recognizing that for a stable orbit Coulomb's force of attraction is equal and opposite to the centripetal force we get
Using (1) we get
.
Rearranging we get allowed radii as
#r_n=a_0n^2# ......(2)
where#a_0=(4piepsilon_0)/m_e((h)/(2pie))^2=0.0529" nm"# , Bohr's radius.
From (1) and (2) we get allowed velocities as
The required ratio is
#v_4/v_7=7/4=1.75#