Question

Radius of fourth excited state of He+ ion is
(1) 661.25 pm
(2) 6.6125 pm
(3) 423.2 pm
(4) 896.5 pm​

Answer 1

answer : option (1) 661.25 pm

explanation : The lowest energy level shell n = 1 ( it is known as ground state of ions ).

first excitated state, electron moves from ground state (n = 1) to n = 2.

so, for first excitated state, we consider n = 2

similarly, for 2nd excited state, we consider n = 3

....

and then, fourth excited state , we should consider n = 5

now according to Bohr's atomic model,

r = 0.529 × n²/Z A°

for He+ ion, Z = 2

so, radius of fourth excited state, r = 0.529 × (5)²/2 = 6.6125 A°

[ we know, 100 pm = 1A° ]

then, r = 6.6125 × 100 pm = 661.25 pm

hence, option (a) is correct choice.