Atoms , molecules & nuclei

By Prof. Smt Sanchita Jadhav Yadav Prof. Mr .Vipinkumar Yadav

Geiger – Marsden Experiment

Rutherford’s Model of Atom

Bohr’s Theory of Hydrogen Atom

Postulate 1: The electron in a hydrogen atom revolves in circular orbit around the nucleus with nucleus as the centre of the orbit. The necessary centripetal force for circular motion is provided by electrostatic force of attraction between the positively charged nucleus & negatively charged electron.

Postulate 2: The electron revolves round the nucleus only in those orbits for which the angular momentum is equal to an integral multiple of h/2π , where h is planck’s constant.

Angular momentum=Iω• ω = v/

r• Iω=

mr2(v/r)=mvr

By 2nd postulateAngular

momentum= n(h/2π)

mvr=n(h/2π)Where

n=1,2,3,4…n is called principal quantum number

Postulate 3: when electrons jumps from orbit of higher energy to an orbit of lower energy, it radiates energy in the form of photon.

Initial

higher

energy

orbit has

principal

quantum

number

= n

Final

orbit on

which

the

electron

s jumps

has

principal

quantum

number

= p

En-Ep = hvV=

frequency

of emitt

ed radiation.

Hydrogen spectrum

When a gas is heated or

subjected to strong electric field or

suitable radiation , it begins to emit electromagnetic waves of specific

wavelength called characteristics

spectrum of gas.

Balmer observed and measured the wavelength of

emitted radiation.

But he could not explain

theoretically the real cause of hydrogen spectrum.

It was Bohr who gave satisfactory

theoretical explanation of the origin of Balmer

lines and also predicted

possibility of other lines in the

hydrogen spectrum.

1.Lyman series: This series arises due to transitions of electrons from

different outer orbits to the first Bohr’s orbit (p = 1). Therefore the wavelength for Lyman series is given by

n = 2,3,4……

For n = 2 & 3 , the wave lengths are 1216 AU & 1025 AU respectively i.e this series lies in the ultra violet region of electromagnetic spectrum.

2.Balmer series: This series arises due to transitions of electrons from

different outer orbits to the second Bohr’s orbit (p = 2). Therefore the wavelength for Balmer series is given by n = 3,4……

For n = 3 & 4 , the wave lengths are 6563 AU & 4868 AU respectively i.e this series lies in visible region of electromagnetic spectrum.

3.Paschen series: This series arises due to transitions of electrons from

different outer orbits to the third Bohr’s orbit (p = 3). Therefore the wavelength for Paschen series is given by n = 4,5,6,7……

For n = 4 & 5 , the wavelengths are 18750 AU & 12820 AU respectively i.e this series lies in infrared region of electromagnetic spectrum.

4.Brackett series: This series arises due to transitions of electrons from

different outer orbits to the fourth Bohr’s orbit (p = 4). Therefore the wavelength for Brackett series is given by n = 5,6,7……

For n = 5 & 6 , the wavelengths are 40518 AU & 26253 AU respectively i.e this series lies near infrared region of electromagnetic spectrum.

5.Pfund series: This series arises due to transitions of electrons from

different outer orbits to the fifth Bohr’s orbit (p = 5). Therefore the wavelength for Pfund series is given by n = 6,7……

For n = 6 & 7 , the wavelengths are 75587 AU & 46533 AU respectively i.e this series lies far infrared region of electromagnetic spectrum.

Energy level diagram for hydrogen atom