Question

The radius (in pm) of the 3rd orbit of He+ is Li+2 respectively

Answer 1

the basic formula for calculating the radius of nth orbit is Rn=0.529×(n^2/Z)angstrom where Z is the atomic number of the element.

Thus for 3rd orbit of He+ radius is(0.529×(3^2))/2=2.3805angstrom

and for Li2+it will be (0.529×9)/3=1.587 angstrom

Answer 2

Given:

Two ions He+ and Li+2.

To Find:

The radius of the 3rd orbit of He+ and Li+2 is?

Solution:

1. The Bohr's radius of an  atom is given by the formula,

=> Bohr's Radius = $\frac{n^2* 0.529}{z}$  A° ( A° = Armstrongs ),

2. Calculate the Bohr's radius using the above formula,

=> He+ ion:

=> Z = 2, n = 3,

=> r = (3)² x 0.529/2,

=> r = 9 x 0.529/2,

=> 4.671/2 A°,

=> 2.3355 A°,

=> 233.55 pm. ( 1pm = 10^-12m)

=> Li+2 ion:

=> Z = 3, n =3,

=> r = (3)² x 0.529/3,

=> r = 3 x 0.529,

=> r = 1.587 A°

=> r = 158.7 pm.

Therefore, the radius of the 3rd orbit of He+ and Li+2 in the pm are 233.55 and 158.7 respectively.