RADIUS OF BOHR'S n^th ORBIT  - FORMULA & RATIOS - SOLVED PROBLEMS
IIT JEE - NEET - CSIR UGC NET - GATE CHEMISTRY

First of all, watch the following video on radius of Bohr's orbit.

Which hydrogen like species will have same radius as that of Bohr's first orbit of hydrogen atom? 

(IIT JEE 2004)

1) n=2, Li²⁺ 

2) n=2, Be³⁺ 

3) n=2, He⁺ 

4) n=3, Li²⁺

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 n²/Z values of orbits for given species with that of hydrogen's first orbit to get the answer.

Solution:

Conclusion:

Since the n²/Z values are same for second orbit of Be³⁺ and first orbit of H, their radii are also equal. Answer is option 2.

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Related questions

1) The radius of Bohr’s first orbit in Li²⁺ is: 

(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=10² pm

Solution:

In picometers, the radius = 0.1763 x 10²  = 17.63 pm

2) The ratio of radii of first three Bohr's orbits in hydrogen atom is:

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 = 0.529n² Å.

For first three orbits, n values are 1,2 and 3. 

Therefore:

The ratio of radii of first three orbits = r₁ : r₂ : r₃ = n₁² : n₂² : n₃² = 1² : 2² : 3² = 1 : 4 : 9

Homework

1) What is the ratio of the radii of first orbits of H, He⁺ and Li²⁺ ?

Answer: 1:1/2:1/3 =6:3:2

2) Is it possible to calculate the radii of orbits in He²⁺ 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 Li²⁺

C) second orbit of Be3⁺

D) None

Answer: option C is correct

6) The ratio of radii of first orbits of He⁺ and Li²⁺ 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 Be³⁺ ion is....... (8 : 1)

9) Bohr atomic radius of 3rd shell of Li²⁺ ion is........( 3 x 0.529 = 1.587 A^o)

10) The atomic radii of first orbit of h-atom 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 &  Li²⁺ ion. 

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