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

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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