First slide

Bohr Model of the Hydrogen atom.

Question

The spectrum of a hydrogen - like ion in the Third Balmer line has a wavelength of 108.5 nm. Then number of protons in the nucleus of the ion is

Easy

A

4
B

5
C

3
D

2

Solution

(4)
For the Third Balmer line,
$\begin{array}{l} \frac{h c}{λ} = Δ E = 13.6 \times Z^{2} \times (\frac{1}{2^{2}} - \frac{1}{5^{2}}) \\ ∴ \frac{12420}{1085} = 13.6 \times Z^{2} \times \frac{21}{100} \Rightarrow Z = 2 \end{array}$

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