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  • Estimate the ratio of the wavelengths associated with the electron orbiting around the nucleus in the ground and second excited states of hydrogen atom.   

Estimate the ratio of the wavelengths associated with the electron orbiting around the nucleus in the ground and second excited states of hydrogen atom. 

 

Answers (1)

The wavelength can be found by De Broglie wavelength equation

For electron, the ground state n = 1

By de Broglie's equation, n\lambda =2\pi r_n

where, r_n  is the radius of the ground state.

r_n=n^2\left ( \frac{h^2\epsilon _0}{\pi me^2} \right )

        =1\times 0.529\AA

         = 0.529\AA

Therefore, \lambda =2\times 3.14\times 0.529=3.32\AA

For second state, n=3

So, n\lambda =2\pi r_n

r_n=n^2\times 0.529=9\times 0.529=4.761\AA

Therefore, 3\times \lambda =2\times 3.14\times 4.761

\lambda =\frac{29.899}{3}=9.966\AA

Ratio =\frac{3.325}{9.966}=0.33

The ratio of the wavelength is 0.33

Posted by

Safeer PP

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