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

Write unit of Rydberg constant and derive the relation for wave number

(\frac{1}{λ}), \frac{1}{λ} = Z^{2} R (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})

and write the symbols stands for.

Accepted Answer

The energy of the electron in the nth orbit is given by,

$E = - \frac{m Z^{2} e^{4}}{8 {ε_{0}}^{2} h^{2} n^{2}}$

Suppose in the excited atom, an electron jumps from some higher energy state $n_{2}$ to a lower energy level state $n_{1}$ . The energy difference between these states is

$E_{2} - E_{1} = \frac{m Z^{2} e^{4}}{8 {ε_{0}}^{2} h^{2}} (\frac{1}{{n_{1}}^{2}} - \frac{1}{{n_{2}}^{2}})$

According to Bohr's third postulate, the frequency of the electromagnetic wave or photon is

$v = \frac{E_{2} - E_{1}}{h} = \frac{m Z^{2} e^{4}}{8 {ε_{0}}^{2} h^{3}} (\frac{1}{{n_{1}}^{2}} - \frac{1}{{n_{2}}^{2}})$

The corresponding wavelength of the emitted radiation is given by,

$\frac{1}{λ} = \frac{v}{c} = \frac{m Z^{2} e^{4}}{8 {ε_{0}}^{2} c h^{3}} (\frac{1}{{n_{1}}^{2}} - \frac{1}{{n_{2}}^{2}}) \frac{1}{λ} = \frac{v}{c} = R Z^{2} (\frac{1}{{n_{1}}^{2}} - \frac{1}{{n_{2}}^{2}}) Where, R = \frac{m e^{4}}{8 {ε_{0}}^{2} c h^{3}} called Rydberg constant$

The unit of the Rydberg constant is $m^{- 1}$ .

Rydberg constant, $R = \frac{m e^{4}}{8 {ε_{0}}^{2} c h^{3}}$

Where, $e =$ Electronic charge

$m =$ Mass of the electron

$c = 3 \times 10^{8} m / s$ The speed of the light

$h = 6.67 \times 10^{- 34} Js$ Planck's constant

Write unit of Rydberg constant and derive the relation for wave number $(\frac{1}{λ}), \frac{1}{λ} = Z^{2} R (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$ and write the symbols stands for.

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

Learn and Prepare for any exam you want !

Write unit of Rydberg constant and derive the relation for wave number 1λ,1λ=Z2R1n12−1n22 and write the symbols stands for.

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

Learn and Prepare for any exam you want !

Write unit of Rydberg constant and derive the relation for wave number $(\frac{1}{λ}), \frac{1}{λ} = Z^{2} R (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$ and write the symbols stands for.