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Energy of an electron in hydrogen atom i...

Energy of an electron in hydrogen atom is given as :
`E_n = -(2 pi^2 me^4)/(n^2 h^2) = -(1.312 xx 10^6)/(n^2) J mol^(-1)`
(i) Calculate the ionisation energy of H-atom.
(ii) Compare the shortest wavelength emitted by hydrogen atom and `He^(+)` ion.

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To solve the given question, we will break it down into two parts as specified. ### Part (i): Calculate the ionization energy of H-atom. 1. **Understanding Ionization Energy**: Ionization energy is the energy required to remove an electron from an atom in its ground state to an infinite distance (where the electron is no longer bound to the atom). Mathematically, it can be expressed as: \[ \text{Ionization Energy} = E_{\infty} - E_1 ...
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Bohr's model enables us to derive the energy of an electron revolving in nth orbit. For H-atom and hydrogen like species : E_n = (2 pi^2 m e^4 Z^2)/(n^2 h^2) or = - (13.6 Z^2)/(n^2) eV "atom"^(-1) = (21.8 xx 10^(-19) Z^2)/(n^2) J "atom"^(-1) This helps to calculate the radius of an orbit, r_n = (0.529 n^2)/(Z) Å Bohr's model also explains the occurrence of different spectral lines. The wavelengths of difference line can be given as : 1/lambda = barv ("in" cm^(-1)) = R (1/(n_1^2) - 1/(n_2^2)) R = 109678 cm^(-1) and n_2 > n_1 . What is the experimental evidence in support of the fact that electronic energies in an atom are quantized ?

Bohr's model enables us to derive the energy of an electron revolving in nth orbit. For H-atom and hydrogen like species : E_n = (2 pi^2 m e^4 Z^2)/(n^2 h^2) or = - (13.6 Z^2)/(n^2) eV "atom"^(-1) = (21.8 xx 10^(-19) Z^2)/(n^2) J "atom"^(-1) This helps to calculate the radius of an orbit, r_n = (0.529 n^2)/(Z) Å Bohr's model also explains the occurrence of different spectral lines. The wavelengths of difference line can be given as : 1/lambda = barv ("in" cm^(-1)) = R (1/(n_1^2) - 1/(n_2^2)) R = 109678 cm^(-1) and n_2 > n_1 . What is the ratio of radius of 4th orbit of hydrogen and 3rd orbit of Li^(2+) ion ?