Atomic structure

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## Atomic structure- numerical

### Solution )

m = 9.1 x 10-28 gm , v = 105 cm/sec , h = 6.625 x 10 -27 erg

Kinetic energy = mv2 / 2

= 9.1 x 10-28 x 105 x 105 / 2

K E = 4.55 x  10-18 erg Ans.

λ = h / mv = 6.625 x 10 -27  / 9.1 x 10-28 x 10 5

### Solution )

E1 = – 5.42 x 10-12 ergs

E2 = – 2.41  x 10-12 ergs

Δ E = E2 – E1 = – 2.41  x 10-12 – (- 5.42  x 10-12)

Δ E = 3.01 x 10 -12 ergs

λ = hc / ΔE

h = 6.625 x 10-27 , c = 3 x 10 10 cm /sec

λ = 6.625 x 10-27 x 3 x 10 10 / 3.01 x 10 -12

### Solution )

Radius  of atom = 10-8 cm

Radius  of nucleus = 10-13 cm

volume of atom = 4 π r3/3 = 4 x π x 10-8 x 10-8 x 10-8 /3

volume of nucleus =  4 π r3/3 = 4 x π x 10-13 x 10-13 x 10-13 /3

volume of nucleus / volume of atom = [4 x π x 10-13 x 10-13 x 10-13 /3]/ [4 x π x 10-8 x 10-8 x 10-8 /3]

### Solution )

n1 = 1 (ground state)

n2 = 3

#### 1 / λ =  RH [( 1/ n12) – ( 1/ n22)]

λ = c / v

v = RH. c [( 1/ n12) – ( 1/ n22)]

=  109737 x 3 x 1010 [( 1/ 12) – ( 1/ 32)] =

= 329211 x 1010 [( 1/ 1) – ( 1/ 9)]

### Solution )

#### 1 / λ =  RH [( 1/ n12) – ( 1/ n22)]

For Lyman series , n1 = 1

Given , n2 = 4