Question #95620
a) Calculate the energy required to ionize a ground state hydrogen atom. Report your answer in kilojoules.Answer in Kj
b)What is the longest wavelength of electromagnetic radiation capable of ionizing a ground state hydrogen atom? Report your answer in nanometers.
c)Calculate the energy required to ionize a hydrogen atom to an excited state where the electron is initially in the n = 5 energy level. Report your answer in kilojoules.
d)What is the longest wavelength of electromagnetic radiation capable of ionizing this hydrogen atom in an excited state? Report your answer in nanometers.
b)What is the longest wavelength of electromagnetic radiation capable of ionizing a ground state hydrogen atom? Report your answer in nanometers.
c)Calculate the energy required to ionize a hydrogen atom to an excited state where the electron is initially in the n = 5 energy level. Report your answer in kilojoules.
d)What is the longest wavelength of electromagnetic radiation capable of ionizing this hydrogen atom in an excited state? Report your answer in nanometers.
Expert's answer
1. The energy of shells in a hydrogen atom is calculated by the formula E = -Eo/n^2 where n is any integer, and Eo = 2.179X10^-18 J. So, the energy of a ground state electron in hydrogen is:
E = -2.179X10^-18 J / 1^2 = -2.179X10^-21 kJ
Consequently, to ionize this electron would require the input of 2.179X10^-21 kJ
2. The wavelength of a photon with this energy would be:
Energy = hc/wavelength
wavelength = hc/energy
wavelength = 6.626X10^-34 Js (2.998X10^8 m/s) / 2.179X10^-18 J = 9.116X10^-8 m
Converting to nanometers gives: 91.16 nm
3. Repeat the calculation in 1, but using n=5.
4. Repeat the calculation in 2 using the energy calculated in 3.
