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Question

please help with the following questions (part d and e only) based on the question in the picture

d. Find an expression for the velocity of the electron at each energy level. Calculate
the velocity of the electron at the lowest energy level.

e. Assume a hypothetical ion with Z protons, no neutrons and one electron. Above
which Z the velocity of the electron exceeds the speed of light? can such an atom
exist?

Consider a Helium ion (Z = 2) with one electron. a. Derive the energy levels of the this ion. b. Calculate the ionisation energy. c. Calculate the 5 main wavelengths of the principal series, namely the wavelength that corresponds to the transitions n → 1, with n = = 2, 3, 4, 5, 6. Plot them as spectral lines. d. Find an expression for the velocity of the electron at each energy level. Calculate the velocity of the electron at the lowest energy level. e. Assume a hypothetical ion with Z protons, no neutrons and one electron. Above which Z the velocity of the electron exceeds the speed of light? can such an atom exist?
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Transcribed Image Text:Consider a Helium ion (Z = 2) with one electron. a. Derive the energy levels of the this ion. b. Calculate the ionisation energy. c. Calculate the 5 main wavelengths of the principal series, namely the wavelength that corresponds to the transitions n → 1, with n = = 2, 3, 4, 5, 6. Plot them as spectral lines. d. Find an expression for the velocity of the electron at each energy level. Calculate the velocity of the electron at the lowest energy level. e. Assume a hypothetical ion with Z protons, no neutrons and one electron. Above which Z the velocity of the electron exceeds the speed of light? can such an atom exist?
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