First slide

Bohr's atom model

Question

An atom emits a spectral line of wavelength $λ$ when an electron makes a transition between levels of energy $E_{1}$ and $E_{2}$ . Which expression correctly relates $λ$ , $E_{1}$ and $E_{2}$ ?

Moderate

A

$λ = \frac{h c}{E_{1} + E_{2}}$
B

$λ = \frac{2 h c}{E_{1} + E_{2}}$
C

$λ = \frac{2 h c}{E_{1} - E_{2}}$
D

$λ = \frac{h c}{E_{1} - E_{2}}$

Solution

By quantum theory of radiation, the energy change $∆ E$ between energy levels is proportional to the frequency of electromagnetic radiation f and is given by
$Δ E = h f = \frac{h c}{λ}$
$Hence, λ = \frac{h c}{Δ E} = \frac{h c}{E_{1} - E_{2}}$

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