(A) The frequency $f$ of the emitted radiation is given by $f = c / \lambda = cR [1/(n-1)^2 - 1/n^2]$.Simplifying the expression: $f = Rc [n^2 - (n-1)

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(A) The frequency $f$ of the emitted radiation is given by $f = c / \lambda = cR [1/(n-1)^2 - 1/n^2]$.Simplifying the expression: $f = Rc [n^2 - (n-1)^2] / [n^2(n-1)^2]$.$f = Rc [n^2 - (n^2 - 2n + 1)] / [n^2(n-1)^2] = Rc (2n - 1) / [n^2(n-1)^2]$.Since $n >> 1$,we can approximate $(n-1) \approx n$ and $(2n - 1) \approx 2n$.Substituting these approximations: $f \approx Rc (2n) / [n^2(n^2)] = 2Rc / n^3$.Therefore,$f \propto 1/n^3$.

Class 12 Physics Atoms Electron Energy and Electron Energy Levels in Hydrogen Atom

Difficult

In a hydrogen-like atom,an electron makes a transition from an energy level with principal quantum number $n$ to another with principal quantum number $(n - 1)$. If $n >> 1$,the frequency of the emitted radiation is proportional to:

A
$\frac{1}{n^3}$
B
$\frac{1}{n}$
C
$\frac{1}{n^2}$
D
$\frac{1}{n^{3/2}}$

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Electron Energy and Electron Energy Levels in Hydrogen Atom

If $n$ is the orbit number of the electron in a hydrogen atom,the correct statement among the following is

EasyKCET 2012

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As per the given figure,$A$,$B$,and $C$ are the first,second,and third excited energy levels of a hydrogen atom,respectively. If the ratio of the two wavelengths (i.e.,$\frac{\lambda_1}{\lambda_2}$) is $\frac{7}{4n}$,then the value of $n$ will be

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The $1^{st}, 2^{nd},$ and $3^{rd}$ energy levels of an atom are $E, 4E/3,$ and $2E$ respectively. If a wavelength $\lambda$ is emitted during the transition $3 \to 1$,what is the wavelength emitted during the transition $2 \to 1$?

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How much energy is needed to release the electron from the second excited state in the hydrogen atom (in $eV$)?

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What is the total energy of an electron at an infinite distance from the nucleus in an atom?

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In a hydrogen-like atom,an electron makes a transition from an energy level with principal quantum number $n$ to another with principal quantum number $(n - 1)$. If $n >> 1$,the frequency of the emitted radiation is proportional to:

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