# Atomic Structure - 2

__ Calculation of radius of orbit__:

__:__

**Derivation**Electrons revolves in orbit.

Centripetal force acting on electron away from centre & force of attraction towards centre.

For electron to revolve in same orbit.

[ = 1 in CGS unit] ………………….. (i)

mvr = n ………………………………………………. (ii)

v =

Putting value of v from eq. (ii) in eq. (i)

……………………………………………. (iii)

r

_{0}= = 0.529 A

^{0}Bohr radius

For H-atom, r_{n} = n^{2} x r_{0} = n^{2} x 0.529 A^{0} |

For H-like atom, like He

^{+},

__:__

**Calculation energy of electron**Total energy of electron (E) = K.E. + P.E.

= mv

^{2}-

__: Why P.E. is - ?__

**Dumb Question**Ans: P.E. is work done when electron moves from to r.

P.E. =

__: Why Force is -ve ?__

**Dumb Question**Ans: Force is work attractive. So, it is taken as -ve.

From eq. (i) mv

^{2}=

E = - = -

__: What does -ve sign signify ?__

**Dumb Question**Ans: -ve sign show’s that electron is bound to that orbit & atom.

E = -

Substituting value of r from eq. (iii)

………………

__:__

**Calculation of velocity of electron in any orbit**Substituting value of r from (ii) in (i)

v =

For H-like atom,

v

_{n}= x 2.188 x 10

^{8}cms

^{-1}

For H-atom, putting z = 1

v

_{n}= cms

^{-1}

From eq. (i)

v

^{2}=

__:__

**Calculation of no. of revolutions of electron in an orbit per sec**mvr = n v =

No. of rev./sec =

No. of revolutions per sec =

=

__:__

**Calculation of no. of waves in any orbit**No. of waves in any orbit =

= De Broglie relation.

__: It is reciprocal of wavelength.__

**Waver no.**For H-atom (wave no.) = R R Rydberg constant

R = 1.097 x 10

^{7}m

^{-1}

For Lyman Series n

_{1}= 1, n

_{2}= 2, 3, 4, ……………………………….

For Balmer Series n

_{1}= 2, n

_{2}= 3, 4, 5, ……………………………….

For Paschen Series n

_{1}= 3, n

_{2}= 4, 5, 6, ……………………………….

For Brackett Series n

_{1}= 4, n

_{2}= 5, 6, 7, ……………………………….

For Pfund Series n

_{1}= 5, n

_{2}= 6, 7, 8, ……………………………….

For H-like atom,

= Rz

^{2}

z - atomic No.

when n

_{2}in Redbergis formula is i.e. n

_{2}=

__:__

**De Broglie Relation**Matters have dual nature of particle & wave If assumed as wave, its energy.

E = h Plank’s quantum theory ……………………………… (i)

If assumed as particle, its energy.

E = mc

^{2}Einstein Eq. ………………………………………….. (ii)

Equating (1) & (2)

h = mc

^{2}

sinc =

h = mc

^{2}

= |

Deg broglie pointed that this eq. can be applicable to any particle.

= =

= de broglie wavelength.