Question

Using Bohr atomic model, drive expression for calculating the radius of orbits (5)
in He+. Using this expression, calculate the radius of fourth orbit of He+ ion.

Answer 1

according to Bohr's model of atom
★ angular momentum of an electron an orbital is integral multiple of h/2π
e.g mvr = nh/2π

★ electron revolve around the nucleus electrostatic force is balanced by centripetal force .
e.g KZe²/r² = mv²/r

by both equation ,
n = n²h²/4π²mKZe²

= (h²/4π²mKe²) (n²/Z)

value of h²/4π²mKe² = 0.529 A°

so, radius of nth orbit = (0.529)n²/z A°

now ,radius of 4th orbit of He+
= (0.529)(4)²/2 = 0.529× 8 A°