Name: Bohr's Model for the Hydrogen Atom
Uploaded: 2019-07-19
Duration: 4 min 50 s
Description: Why don't the revolving electrons in an atom not collide with any protons? Why do different elements emit a different colour? Let's study Bohr's hydrogen ato...

Question

Show that the shortest wavelength lines in Lyman, Balmer and Paschen series have their wavelengths in the ratio

1 : 4 : 9

.

Accepted Answer

Wavelength of any series is shortest when transition of electron happens from infinite to the corresponding orbit.
For Lyman series, $n_{1} = 1$ and $n_{2} = \infty$
Therefore, the wavelength, $\frac{1}{λ_{1}} = R (\frac{1}{1^{2}} - \frac{1}{\infty}) \Rightarrow λ_{1} = \frac{1}{R}$ .......( $1$ )
For Balmer series, $n_{1} = 2$ and $n_{2} = \infty$
Therefore, the wavelength, $\frac{1}{λ_{2}} = R (\frac{1}{2^{2}} - \frac{1}{\infty}) \Rightarrow λ_{2} = \frac{4}{R}$ ......( $2$ )
For Paschen series, $n_{1} = 3$ and $n_{2} = \infty$ , $\frac{1}{λ_{3}} = R (\frac{1}{3^{2}} - \frac{1}{\infty}) \Rightarrow λ_{3} = \frac{9}{R}$ ......( $3$ )
From equation ( $1$ ), ( $2$ ) and ( $3$ ) ,

$λ_{1} : λ_{2} : λ_{3} = 1 : 4 : 9$

Show that the shortest wavelength lines in Lyman, Balmer and Paschen series have their wavelengths in the ratio $1 : 4 : 9$ .

Important Questions on Atoms

Learn and Prepare for any exam you want !

Show that the shortest wavelength lines in Lyman, Balmer and Paschen series have their wavelengths in the ratio 1:4:9.

Important Questions on Atoms

Learn and Prepare for any exam you want !

Show that the shortest wavelength lines in Lyman, Balmer and Paschen series have their wavelengths in the ratio $1 : 4 : 9$ .