Atoms and Nuclei Part 1

In hydrogen atom,
En=

−E0

n2

Where E0 is Ionisation Energy of H.
→ For transition from ( n+1) to n, the energyof emitted radiation is equal to the difference in energies of levels.
ΔE=En+1−En
ΔE=E0(

1

n2

−

1

(n+1)2

)
ΔE=hv=E0(

(n+1)2−n2

n2(n+1)2

)
hv=E0[2n+1n4(1+

1

n

)2]
hv=E0[

n(2+ 1 n )

n4(1+ 1 n )2

]
since n>>>1
Hence,

1

n

≃0
hv=E0[

2

n3

]
v α

1

n3