RADIUS OF BOHR'S nth 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:

 1st orbit of H atom Option 1 n=2, Li2+ Option 2 n=2, Be3+ Option 3 n=2, He+ Option 4 n=3, Li2+ n = 1 2 2 2 3 Z = 1 3 4 2 3 n2/Z 12/1 = 1 22/3 = 4/3 22/4 = 1 22/2 = 2 32/3 = 3

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.

Related questions

1) The radius of Bohrâ€™s first orbit in Li2+ is:

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 nth orbit, rn = 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+ ?

2) Is it possible to calculate the radii of orbits in He2+ using Bohr's equation?

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

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 Ao)

10) The atomic radii of first orbit of h-atom is 0.529 Ao. 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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