Ground State
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Exercise:
The energy of the ground state of the hydrogen atom is given by E_ -frace^ m_eepsilon_^ h^ EgrO abcliste abc Verify the numerical value. abc Show that the energy of the ground state can be expressed as E_ -frachbar^ m_e a_^ abcliste
Solution:
abcliste abc E_ -fracnce^times ncmetimes ncepsO^ times nch^ EJ EeVP abc Plugging the expression for the Bohr radius a_ fracpi epsilon_ hbar^m_e e^ o the above expression for the energy yields E_ -frachbar^ m_e a_^ -frachbar^ m_e fracm_e^ e^pi^ epsilon_^ hbar^ -fracm_e e^pi^epsilon_^hbar^ -fracm_e e^ epsilon_^ pi hbar^ -fracm_e e^ epsilon_^ h^ abcliste
The energy of the ground state of the hydrogen atom is given by E_ -frace^ m_eepsilon_^ h^ EgrO abcliste abc Verify the numerical value. abc Show that the energy of the ground state can be expressed as E_ -frachbar^ m_e a_^ abcliste
Solution:
abcliste abc E_ -fracnce^times ncmetimes ncepsO^ times nch^ EJ EeVP abc Plugging the expression for the Bohr radius a_ fracpi epsilon_ hbar^m_e e^ o the above expression for the energy yields E_ -frachbar^ m_e a_^ -frachbar^ m_e fracm_e^ e^pi^ epsilon_^ hbar^ -fracm_e e^pi^epsilon_^hbar^ -fracm_e e^ epsilon_^ pi hbar^ -fracm_e e^ epsilon_^ h^ abcliste