Question

If, in
1/λ=Ry(1/n21 -1/n22)
you set n1 = 1 and taken2 greater than 1, you generate what is knownas the Lyman series.
a) Find the wavelength of the first member of this series. Thevalue of h is 1.05457 e -34 J*s; the Rydberg constantfor hydrogen is 1.09735 e7 m-1 ; the Bohr radius is5.29177 e-11 m; and the ground stae energy for hydrogen is 13.6057eV.
Answer in units of nm.
b) Consider the next three members of this series. Thewavelengths of successive members of the Lyman series approach acommon limit as n2 → [infinity]. What is thislimit?
Answer in units of nm.

Answer 1

Answer:

a)   λ = 121.5 nm , b) 102.6, 97, 91.1 nm

Explanation:

Bohr's model describes the energy of the hydrogen atom

      $E_{n}$ = k² e² / 2m (1 / n²)

A transition occurs when the electron passes from n level to a lower one

       $E_{i}$ -  $E_{n}$ = k² e² / 2m (1 / $n_{i}$² - 1 /  $n_{f}$²)

Planck's relationship is

        E = h f = h c / lam

        hc /λ =  k² e²/ 2m(1 / $n_{i}$² - 1 /  $n_{f}$²)

        1 / λ = [k² e² / 2m h c] (1 / $n_{i}$² - 1 /  $n_{f}$²)

        1 /λ = Ry] (1 / $n_{i}$² - 1 /  $n_{f}$²)

a) the first element of the series occurs for $n_{f}$ = 2

        1 / λ = 1.097 10⁷ (1- 1/2²)

        1 / λ = 1.097 10⁷ (1- 0.25)

        1 / λ = 0.82275 10⁷

        λ = 1.215 10⁻⁷ m

        λ = 1,215 10⁻⁷ m (10⁹nm / m)

        λ = 121.5 nm

b) the next elements of the series occur to

$n_{f}$       $n_{i}$    1 /λ                            λ (10-7m)       λ (nm)

3        1     1,097 10⁷ (1-1 / 9)     1,0255           102.6

4        1     1,097 10⁷ (1-1 / 16)   0.9723            97.2

∞       1      1,097 10⁷ (1 - 0)     0.91158           91.1