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Find the Wavelength of the Electron Orbiting in the First Excited State in Hydrogen Atom. - Physics

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प्रश्न

Find the wavelength of the electron orbiting in the first excited state in hydrogen atom.

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उत्तर

For first excited state hydrogen atom is n = 2

Energy of the electron in nth orbit = `−13.6/n^2 eV`

`=13.6/2^2=3.4 eV`

`"Energy" =(hc)/λ=1240/λ`

`3.4 = 1240/λ`
`⇒λ = 364.7 nm`

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The Line Spectra of the Hydrogen Atom
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2016-2017 (March) Delhi Set 2

संबंधित प्रश्‍न

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(a) Construct a quantity with the dimensions of length from the fundamental constants e, me, and c. Determine its numerical value.

(b) You will find that the length obtained in (a) is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr to discard c and look for ‘something else’ to get the right atomic size. Now, the Planck’s constant h had already made its appearance elsewhere. Bohr’s great insight lay in recognising that h, me, and e will yield the right atomic size. Construct a quantity with the dimension of length from h, me, and e and confirm that its numerical value has indeed the correct order of magnitude.


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