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Let the wavefunction of the electron in a hydrogen atom bewhere are the eigenstates of the hamiltonian in the standard nutation. The expectation value of the energy in this state is
  • a)
    −10.8 eV
  • b)
    −6.2 eV
  • c)
    −9.5 eV
  • d)
    −5.1 eV
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Let the wavefunction of the electron in a hydrogen atom bewhereare the...
We have:

This wave function is normalized as if we do:

The expectation value of the energy in this state is:

We can find the E's first we get:

corresponding all wavefunctions.
Now, we can find the expectation value to be:

Solving it we will get:
<E>=−5.1eV.
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Let the wavefunction of the electron in a hydrogen atom bewhereare the eigenstates of the hamiltonian in the standard nutation. The expectation value of the energy in this state isa)−10.8 eVb)−6.2 eVc)−9.5 eVd)−5.1 eVCorrect answer is option 'D'. Can you explain this answer?
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Let the wavefunction of the electron in a hydrogen atom bewhereare the eigenstates of the hamiltonian in the standard nutation. The expectation value of the energy in this state isa)−10.8 eVb)−6.2 eVc)−9.5 eVd)−5.1 eVCorrect answer is option 'D'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about Let the wavefunction of the electron in a hydrogen atom bewhereare the eigenstates of the hamiltonian in the standard nutation. The expectation value of the energy in this state isa)−10.8 eVb)−6.2 eVc)−9.5 eVd)−5.1 eVCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let the wavefunction of the electron in a hydrogen atom bewhereare the eigenstates of the hamiltonian in the standard nutation. The expectation value of the energy in this state isa)−10.8 eVb)−6.2 eVc)−9.5 eVd)−5.1 eVCorrect answer is option 'D'. Can you explain this answer?.
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