# 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#