Question

solv the first 7 transitions of lyman series. what happens to the energy in transtion when n goes to infinity?

Answer 1

Lyman series is the first series in transition series. For Lyman series n_f=1

We can calculate the wavelength of first 7 transitions by Ryberg formula i.e,

n_{f =} 1 n_i= 2

1/ = R_h (1/n²_f - 1/n_i²) , R_{h = 1.097 x 10}⁷

1/ = 1.097 x 10⁷ (1 - 1/2²)

1/ = 1.097 x 10⁷ (1 - 1/4)

1/ = 1.097 x 10⁷ x 3/4

₁ = 1.217 x 10^-7 m

n_{f =} 1 n_i= 3

1/ = R_h (1/n²_f - 1/n_i²) , R_{h = 1.097 x 10}⁷

1/ = 1.097 x 10⁷ (1 - 1/3²)

1/ = 1.097 x 10⁷ (1 - 1/9)

1/ = 1.097 x 10⁷ x 8/9

₂ = 1.025x 10^-7 m

n_{f =} 1 n_i= 4

1/ = R_h (1/n²_f - 1/n_i²) , R_{h = 1.097 x 10}⁷

1/ = 1.097 x 10⁷ (1 - 1/4²)

1/ = 1.097 x 10⁷ (1 - 1/16)

1/ = 1.097 x 10⁷ x 15/16

₃ = 9.727 x 10^-8 m

n_{f =} 1 n_i= 5

1/ = R_h (1/n²_f - 1/n_i²) , R_{h = 1.097 x 10}⁷

1/ = 1.097 x 10⁷ (1 - 1/5²)

1/ = 1.097 x 10⁷ (1 - 1/25)

1/ = 1.097 x 10⁷ x 24/25

4 = 9.496 x 10^-8 m

n_{f =} 1 n_i= 6

1/ = R_h (1/n²_f - 1/n_i²) , R_{h = 1.097 x 10}⁷

1/ = 1.097 x 10⁷ (1 - 1/6²)

1/ = 1.097 x 10⁷ (1 - 1/36)

1/ = 1.097 x 10⁷ x 35/36

₅ = 9.380 x 10^-8 m

n_{f =} 1 n_i= 7

1/ = R_h (1/n²_f - 1/n_i²) , R_{h = 1.097 x 10}⁷

1/ = 1.097 x 10⁷ (1 - 1/7²)

1/ = 1.097 x 10⁷ (1 - 1/49)

1/ = 1.097 x 10⁷ x 48/49

₆ = 9.310 x 10^-8 m

First we have to calculate wavelength in n level and then at infinity level

n_{f =} 1 n_i= n

1/ = R_h (1/n²_f - 1/n_i²) , R_{h = 1.097 x 10}⁷

1/ = 1.097 x 10⁷ (1 - 1/n²)

1/ = 1.097 x 10⁷ (n² - 1/n²)

= 9.115 x 10^-8 n² / (n² - 1) m

E = hc/

E = 6.626 x 10^-34 x 3 x 10⁸ / 9.115 x 10^-8

E = 2.180 x 10^-18 J

n_{f =} 1 n_i=

1/ = R_h (1/n²_f - 1/n_i²) , R_{h = 1.097 x 10}⁷

1/ = 1.097 x 10⁷ (1 - 1/)

1/ = 1.097 x 10⁷ (1-0 )

= 9.115 x 10^-8 m

E = hc/

E = 6.626 x 10^-34 x 3 x 10⁸ / 9.115 x 10^-8

E = 2.180 x 10^-18 J

When electron moves from higher energy level to lower energy level then the enrgy is emitted in the form of electromagnetic radiation or photons.

The energy thus emitted has a discrete value reason being the shells in an a hydrogen atom are fixed level of energies and thus the energy emmitted by jumping from one level to another level will always be equal to energy required to come back in same level.

So the energy from n to infinity is increasing for example if n_i = 2 then energy required is 1.63 x 10^-18 J and when n_{i =} then energy required is 2.18 x 10^-18 J.