Question

From Bohr's model, derive an expression for the radius of a stationary orbit. Prove that the various stationary orbits are not equally placed​

Answer 1

Answer:

Let the electron of mass m revolves around a nucleus (H-atom) in an orbit of radius r

n

with linear velocity v

n

.

As the electron revolves in an stationary orbit, thus centrifugal force acting on the electron is balanced by the coulombic force i.e. F

centrifugal

=F

coulomb

∴

r

n

mv

n

2

=

r

n

2

ke

2

where k=

4πϵ

o

1

=9×10

9

⟹ r

n

=

mv

n

2

ke

2

Also we use mv

n

r

n

=

2π

nh

Eliminating v

n

from both equations, we get r

n

=

m

ke

2

.

n

2

h

2

4π

2

m

2

r

n

2

⟹ r

n

=

4π

2

mke

2

h

2

n

2

Putting m=9.1×10

−31

kg, h=6.626×10

−34

Js and e=1.6×10

−19

C

We get radius of n

th

Bohr orbit r

n

=0.529 n

2

A

o

Explanation:

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