Name: Bohr Model of the Hydrogen Atom
Uploaded: 2019-07-19
Duration: 4 min 50 s
Description: In this video, we will discuss the Bohr model of the hydrogen atom and electron transition in the hydrogen atom. Get in this to explore more.

Question

Calculate the wavelengths of the third and fifth spectral lines of Paschen series in hydrogen spectrum when

E = \frac{- (2.18 \times 10^{- 18})}{n^{2}}

joule.

Accepted Answer

We are given:

$E = \frac{- (2.18 \times 10^{- 18})}{n^{2}}$

For the third line of Paschen series,the transition will be from: $n_{1} = 3$ to $n_{2} = 6$

$\Rightarrow E_{2} - E_{1} = \frac{- (2.18 \times 10^{- 18})}{{(n_{2})}^{2}} - \frac{- (2.18 \times 10^{- 18})}{{(n_{1})}^{2}}$

$E_{2} - E_{1} = \frac{- (2.18 \times 10^{- 18})}{{(6)}^{2}} - \frac{- (2.18 \times 10^{- 18})}{{(3)}^{2}}$

$= - (2.18 \times 10^{- 18}) [\frac{1}{36} - \frac{1}{9}]$

The energy difference between the two levels will be equal to $\frac{h c}{λ}$

$\Rightarrow \frac{h c}{λ} = 0.1816 \times 10^{- 18}$

$\Rightarrow \frac{6.626 \times 10^{- 34} J s \times 3 \times 10^{8} m s^{- 1}}{λ} = 0.1816 \times 10^{- 18} J$

$∴ λ = 10946 A °$

For the fifth line of Paschen series,the transition will be from: $n_{1} = 3$ to $n_{2} = 8$

$\Rightarrow E_{2} - E_{1} = \frac{- (2.18 \times 10^{- 18})}{{(n_{2})}^{2}} - \frac{- (2.18 \times 10^{- 18})}{{(n_{1})}^{2}}$

$E_{2} - E_{1} = \frac{- (2.18 \times 10^{- 18})}{{(8)}^{2}} - \frac{- (2.18 \times 10^{- 18})}{{(3)}^{2}}$

$= - (2.18 \times 10^{- 18}) [\frac{1}{64} - \frac{1}{9}]$

$\Rightarrow \frac{h c}{λ} = 0.208 \times 10^{- 18}$

$\Rightarrow \frac{6.626 \times 10^{- 34} J s \times 3 \times 10^{8} m s^{- 1}}{λ} = 0.208 \times 10^{- 18} J$

$∴ λ = 9557 A °$

Calculate the wavelengths of the third and fifth spectral lines of Paschen series in hydrogen spectrum when $E = \frac{- (2.18 \times 10^{- 18})}{n^{2}}$ joule.

Important Questions on Atom, Origin of Spectra : Bohr's Theory of Hydrogen Atom

Learn and Prepare for any exam you want !

Calculate the wavelengths of the third and fifth spectral lines of Paschen series in hydrogen spectrum when E=-2.18×10-18n2 joule.

Important Questions on Atom, Origin of Spectra : Bohr's Theory of Hydrogen Atom

Learn and Prepare for any exam you want !

Calculate the wavelengths of the third and fifth spectral lines of Paschen series in hydrogen spectrum when $E = \frac{- (2.18 \times 10^{- 18})}{n^{2}}$ joule.