Solved Examples on Bohr’s Atomic Model
Example 1: If the velocity of an electron of the first orbit in Bohr’s atomic model of a hydrogen atom is 2.19 × 106 m/s. Find the velocity of electrons in the second orbit.
Solution:
Velocity of an electron in orbit n is given by vn = v1/n
Given,
v1 = 2.19 × 106 m/s
n = 2So, v2 = 2.19 × 106 /2
= 1.095 × 106 m/s.
Example 2: The electron in Bohr’s Hydrogen atom, revolves around the nucleus with a speed of 2.18 × 106 m/s in orbit of radius 5.3 × 10-11 m. Find the magnetic field which is produced by electrons on protons in the nucleus.
Solution:
Given,
Radius of orbit, r = 5.3 × 10-11 m
Velocity v= 2.18 × 106 m/s
So, magnetic field, I = Q/T
= e/T
where T = 2πr / v
= (2 × 3.14 × 5.3 × 10-11) / (2.18 × 106)
= 1.528 × 10-16
Therefore,
I = 1.6 × 10-19/ 1.528×10-16
= 1.047 × 10-3 A
Example 3: Find the kinetic energy of an electron in the second Bohr’s orbit of a hydrogen atom.
Solution:
According to Bohr’s postulate
mvr = nh/2π
v = nh/2πmr
K .E = 1/2 mv2
= 1/2 m ( nh / 2πmr ) 2
Example 4: Find the distance between the 2nd and 3rd orbit of Bohr’s atom.
Solution:
Radius of 3rd orbit r3 = 0.529 × n2 × 10-10 / z
= 0.529 × 9 × 10-10
Radius of 2nd orbit r2 = 0.529 × 4 × 10-10
r3 – r2 = 0.529 × (5 × 10 -10)m
= 2.645 A
Example 5: Find the distance between the 2nd and 3rd orbit of Bohr’s atom.
Solution:
Radius of 2nd orbit r2 = 0.529 × n2 × 10-10 / z
= 0.529 × 4 × 10-10
Radius of 1st orbit r1 = 0.529 × 1 × 10-10
r2 – r1 = 0.529 × ( 3 × 10-10) m
= 1.587 A
Bohr’s Model of an Atom
Bohr’s Model is an atomic model proposed by Danish Physicist Niels Bohr in 1913. According to this model, in an atom, the electrons revolve around the nucleus in definite energy levels called orbits/shells. This model provides a basic understanding of the concept of the atom and its constituents.
Let’s learn more about Bhor’s Atomic Model, its limitations, and others in detail in this article.