Question

USING BOHR ATOMIC MODEL DERIVE EXPRESSION FOR CALCULATING THE RADIUS OF ORBIT IN HE.USING THESE EXPRESSION CALCULATE THE FOURTH RADIUS OF ION HE

Answer 1

according to Bohr's theory ,
nh/2π = mvr --------(1)

and KZe²/r² = mv²/r -----------(2)

now, from equation (1)

nh/2π = mvr

v = nh/2πmr
put this in equation (2)

KZe²/r² = m{ nh/2mπr}²/r
KZe²/r² =m.n²h²/4π²m²r³
KZe²/r² = n²h²/4π²mr³

KZe²/r² =n²h²/4π²mr³

r = n²h²/4π²mKZe²
here r is the radius of nth orbit .
where h is plank's constant
m = mass of electrons
K = kappa's constant
e = charge of electron
if you put h, m, K , e , in SI system
then,
r = (0.529)n²/Z A°
now,

radius of 4th orbit of He+ ion =
= (0.529)(4)²/(2) = 0.529 × 8 =4.232 A°