a) Calculate the numerical values of the energies of the first four energy levels in hydrogen in units of both joules (J) and in electron-volts (eV). The first four energy levels are found substituting n = 1, 2, 3, 4 into the equation you found in section (f) above. Show all work. b) Use r = n²ħ²/(e²km) to calculate numerical values for the radii of the first four allowed electron 'orbits' in hydrogen, in units of m. The radius of the 'orbit' closest to the nucleus is called the Bohr radius and is given the symbol ao. (You should notice that each radius is a multiple of the Bohr radius, ie. when n = 1 then r = ao, if n = 2 then r = 2² ao, at n = 3 then r = 9 ao, etc.) c) Summarize your numerical results in the following table; Quantum number n Radius of electron's 'orbit' (m) Electron Energy (J) Electron Energy (eV)

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Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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1. a) Calculate the numerical values of the energies of the first four energy levels in hydrogen in
units of both joules (J) and in electron-volts (eV). The first four energy levels are found
substituting n = 1, 2, 3, 4 into the equation you found in section (f) above. Show all work.
b) Use r = n²ħ²/(e²km) to calculate numerical values for the radii of the first four allowed
electron 'orbits' in hydrogen, in units of m. The radius of the 'orbit' closest to the nucleus is
called the Bohr radius and is given the symbol ao. (You should notice that each radius is a
multiple of the Bohr radius, ie. when n = 1 then r = ao, if n = 2 then r = 2² ao, at n = 3 then r =
9 ao, etc.)
1
2
3
4
c) Summarize your numerical results in the following table;
Quantum number n Radius of electron's 'orbit' (m)
Electron Energy (J)
Electron Energy (eV)
Transcribed Image Text:1. a) Calculate the numerical values of the energies of the first four energy levels in hydrogen in units of both joules (J) and in electron-volts (eV). The first four energy levels are found substituting n = 1, 2, 3, 4 into the equation you found in section (f) above. Show all work. b) Use r = n²ħ²/(e²km) to calculate numerical values for the radii of the first four allowed electron 'orbits' in hydrogen, in units of m. The radius of the 'orbit' closest to the nucleus is called the Bohr radius and is given the symbol ao. (You should notice that each radius is a multiple of the Bohr radius, ie. when n = 1 then r = ao, if n = 2 then r = 2² ao, at n = 3 then r = 9 ao, etc.) 1 2 3 4 c) Summarize your numerical results in the following table; Quantum number n Radius of electron's 'orbit' (m) Electron Energy (J) Electron Energy (eV)
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