First of all, watch the following video on radius of Bohr's orbit.
(IIT JEE 2004)
1) n=2, Li2+
2) n=2, Be3+
3) n=2, He+
4) n=3, Li2+
Radius of Bohr's orbit in hydrogen and hydrogen like species can be calculated by using the following formula.
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.
|1st orbit of H atom||Option 1
|n2/Z||12/1 = 1||22/3 = 4/3||22/4 = 1||22/2 = 2||32/3 = 3|
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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(Aditya vardhan - Adichemistry)
1) 0.0587 pm
2) 17.63 pm
3) 176.3 pm
4) 0.529 pm
Use the following equation to calculate the radius in Angstroms, Å.
Then convert the value into picometers.
Remember 1 Å=102 pm
In picometers, the radius = 0.1763 x 102 = 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 nth orbit, rn = 0.529n2 Å.
For first three orbits, n values are 1,2 and 3.
The ratio of radii of first three orbits = r1 : r2 : r3 = n12 : n22 : n32 = 12 : 22 : 32 = 1 : 4 : 9
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?
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+
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 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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