The formula to calculate the radius of the nth orbit is given by
rn=Zn2...(1)
Substitute proper values of the orbit numbers in order to calculate the formula for the radius of the innermost and third allowed orbital radii.
r1r3====1121...(2)Z329...(3)
Divide equation (2) by equation (3) and solve to calculate the radius of the third allowed orbit.
r3r1r3=====919r19×5.3×10−11m47.7×10−11m4.77A∘