Question

Using Bohr atomic model, drive expression for calculating the radius of orbits
in He+. Using this expression, calculate the radius of fourth orbit of He+ ion.

Answer 1

according to bohr's theory ,
mvr=nh/2pi
v=nh/2pi.mr----------------(1)

and mv^2/r=kZe^2/r^2
put v value from equation (1)
m {n^2h^2/4pi^2m^2r^2}=kZe^2/r

hence
r=n^2h^2/4pi^2kZe^2m
if we write in standard form
ie. r=(0.529).n^2/z angstrum

now
radius of 4th orbit of He+=(0.529)(16/2)A
=4.232 A

Answer 2

according to bohr's theory ,
mvr=nh/2pi
v=nh/2pi.mr----------------(1)

and mv^2/r=kZe^2/r^2
put v value from equation (1)
m {n^2h^2/4pi^2m^2r^2}=kZe^2/r

hence 
r=n^2h^2/4pi^2kZe^2m
if we write in standard form 
ie. r=(0.529).n^2/z angstrum

now 
radius of 4th orbit of He+=(0.529)(16/2)A
=4.232 A