First of all, watch the following video on radius of Bohr's orbit.
(IIT JEE 2004)
1) n=2, Li^{2+}
2) n=2, Be^{3+}
3) n=2, He^{+}
4) n=3, Li^{2+}
Logic:
Radius of Bohr's orbit in hydrogen and hydrogen like species can be calculated by using the following formula.
Where
n = prinicipal quantum number of orbit.
Z = atomic number
Now compare the n^{2}/Z values of orbits for given species with that of hydrogen's first orbit to get the answer.
Solution:
1st orbit of H atom  Option 1 n=2, Li^{2+} 
Option 2 n=2, Be^{3+} 
Option 3 n=2, He^{+} 
Option 4 n=3, Li^{2+} 

n =  1  2  2  2  3 
Z =  1  3  4  2  3 
n^{2}/Z  1^{2}/1 = 1  2^{2}/3 = 4/3  2^{2}/4 = 1  2^{2}/2 = 2  3^{2}/3 = 3 
Conclusion:
Since the n^{2}/Z values are same for second orbit of Be^{3+} and first orbit of H, their radii are also equal. Answer is option 2.
(new) Click here to see 3d Interactive Solved Question paper
(Aditya vardhan  Adichemistry)
1) 0.0587 pm
2) 17.63 pm
3) 176.3 pm
4) 0.529 pm
Logic:
Use the following equation to calculate the radius in Angstroms, Å.
Then convert the value into picometers.
Remember 1 Å=10^{2} pm
Solution:
In picometers, the radius = 0.1763 x 10^{2} = 17.63 pm
1) 1 : 4 : 9
2) 1 : 2 : 3
3) 1 : 2 : 4
4) 9 : 4 : 1
Logic and Solution:
Atomic number, Z is equal to 1.
Hence the radius of n^{th} orbit, r_{n} = 0.529n^{2} Å.
For first three orbits, n values are 1,2 and 3.
Therefore:
The ratio of radii of first three orbits = r_{1 }: r_{2 }: r_{3} = n_{1}^{2} : n_{2}^{2 }: n_{3}^{2} = 1^{2} : 2^{2} : 3^{2} = 1 : 4 : 9
1) What is the ratio of the radii of first orbits of H, He^{+} and Li^{2+} ?
Answer: 1:1/2:1/3 =6:3:2
2) Is it possible to calculate the radii of orbits in He^{2+} using Bohr's equation?
Answer: Yes
3) What is the ratio of circumferences of first three orbits in hydrogen atom?
4) Calculate the radius of 2nd orbit in He^{+}.
5) The radius of which of the following orbit is same as that of first orbit of hydrogen atom....
A) second orbit of He^{+}
B) first orbit of Li^{2+}
C) second orbit of Be3^{+}
D) None
Answer: option C is correct
6) The ratio of radii of first orbits of He^{+} and Li^{2+} is...... (3:2)
7) The ratio of radii of first shell of H atom and that of fourth shell of He^{+} ion is........ (1:8)
8) The ratio of radius of fourth orbit of He^{+} ion to the radius of second orbit of Be^{3+} ion is....... (8 : 1)
9) Bohr atomic radius of 3rd shell of Li^{2+} ion is........( 3 x 0.529 = 1.587 A^{o})
10) The atomic radii of first orbit of hatom is 0.529 A^{o}. The radii of second orbit of He^{+} is.........
11) Derive the relationship between the nth bohr radius of hydrogen atom & Li^{2+} ion.