Question

If, in

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