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Standard XII

Chemistry

Multi-Electron Configurations and Orbital Diagrams

An electron o...

Question

An electron of mass $^{'} m^{'}$ is confined to a one dimensional box of length $^{'} l^{'}$ . If it makes a radiative transition from the second excited state to the ground state, the frequency of the photon emitted is:

\frac{9 h}{8 m l^{2}}

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\frac{3 h}{8 m l^{2}}

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\frac{h}{m l^{2}}

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\frac{2 h}{8 m l^{2}}

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Solution

The correct option is C $\frac{h}{m l^{2}}$
Energy of nth state $= \frac{n^{2} h^{2}}{8 m l^{2}}$
$\Rightarrow E_{g} = \frac{h^{2}}{8 m l^{2}}$ ,
$E_{2 n d e x c i t e d} = E_{3} = \frac{(3)^{2} h^{2}}{8 m l^{2}} = \frac{9 h^{2}}{8 m l^{2}}$

Energy of transition $= E_{3} - E_{g}$
$= \frac{9 h^{2}}{8 m l^{2}} - \frac{h^{2}}{8 m l^{2}} = \frac{8 h^{2}}{8 m l^{2}} = \frac{h^{2}}{m l^{2}}$

$E = h ν \Rightarrow \frac{h^{2}}{m l^{2}} = h ν$
$\Rightarrow ν = \frac{h}{m l^{2}}$

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An electron of mass ′m′ is confined to a one dimensional box of length ′l′. If it makes a radiative transition from the second excited state to the ground state, the frequency of the photon emitted is:

The correct option is C hml2Energy of nth state =n2h28ml2 ⇒Eg=h28ml2, E2nd excited=E3=(3)2h28ml2=9h28ml2 Energy of transition =E3−Eg =9h28ml2−h28ml2=8h28ml2=h2ml2 E=hν⇒h2ml2=hν ⇒ν=hml2

An electron of mass $^{'} m^{'}$ is confined to a one dimensional box of length $^{'} l^{'}$ . If it makes a radiative transition from the second excited state to the ground state, the frequency of the photon emitted is: