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MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Atoms Molecules and Nuclei Formulae Page 1

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    Bohr's Atom Model

(1)

1st Postulate:

 

Centripetal force = electrostatic force

 

 

mv2

=

1

 

e2

 

 

 

r

4pe0

r2

where m

= mass of an orbiting electron

v

= linear velocity of an orbiting electron

r

= radius of orbit

e0

= permittivity of free space

e

= charge on an electron.

 

 2. 2nd Postulate:

 

Angular momentum of an orbiting electron 

= Integral multiple of

mn r

=

nh

 

2p

 

where m

= mass of an orbiting electron

v

= linear velocity of an orbiting electron

r

= radius of orbit

n

= 1, 2, 3, (integer)

h

= Planck's constant.

 

 3. Energy of Photon Emitted or Absorbed is Given by:

 

En2 - En1 = hu

 

where En2 , En1 = final and initial energy levels

 

u = frequency of radiation.

 

 4. Radius of nth Orbit of the Electron:

 

rn =

e0 n2 h2

 

p m e2

 

where e0

= permittivity of free space

n

= 1, 2, 3, (Integer)

h

= Planck's constant

m

= mass of an electron

e

= charge on an electron.

 

5. Potential Energy of an Orbiting Electron:

 

P.E. = -

e2

= -

me4

 

 

4pe0r

4 n2 h2e02

 

K.E. energy of the electron

 

K.E.

=

e2

=

me4

 

 

8pe0r

8 n2 h2e02

 

Total energy of an orbiting electron

 

En

= -

e2

= -

me4

 

 

8pe0r

8 e02

n2 h2

 

\ P.E. = - 2 K.E. and T.E. = - K.E.

 

6. Wave Number () of the Electromagnetic Radiation:

 

=

1

=

u

=

me4

1

-

1

 

 

 

 

 

l

c

8e02 h3c

n12

n22

 

\

1

=

R

1

-

1

 

 

 

l

n12

n22

 

where R = Rydberg constant =

me4

 

8e02h3C

 

7. Velocity of the Electron:

 

vn =

e2

1

 

\ vn a

1

 

n

 

 

2he0

n

 

8. Angular Speed of the Electron:

 

wn =

pme4

1

 

\ wn a

1

 

n3

 

 

2h3e02

n3

 

9. Period of the Revolution of the Electron:

 

Tn =

4h3e02

(

n3

)

 

\ Tn a n3

 

me4

 

10. Centripetal Acceleration:

 

a =

pme6

1

 

\ a a

1

 

n4

 

 

4e03h4

n4

 

11. Energy of the Electron in Ground State:

 

for ground state, n = 1

\ E1 =

- me4

 

8h2e02

 

\ E1 = - 13.6 e V

 

12. General Expression for Energy, Radius and Velocity

 

En = E1/n2

rn = r1 . n2

vn = v1 / n

 

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