When all quantum numbers are considered, how many different quantum states are there for a hydrogen atom with n=1 ? with n=2 ? with n=3 ? list the quantum numbers of each state.

Respuesta :

Quantum numbers are:

  • (A) n = 1 ⇒ n -1
  • (B) n = 2 ⇒ n = 2

What do we mean by quantum numbers?

  • Quantum numbers are used in quantum physics and chemistry to describe the values of conserved quantities in the dynamics of a quantum system.
  • Quantum numbers are eigenvalues of operators that commute with the Hamiltonian and their corresponding eigenspaces—quantities that can be known with precision at the same time as the system's energy.
  • A specification of all of the quantum numbers of a quantum system, when combined, fully characterizes the system's basis state and can, in theory, be measured together.

Quantum numbers:

(A) n = 1

  • The electron in a hydrogen atom with n=1 is in its ground state; if the electron is in the n=2 orbital, it is in an excited state.
  • For a given n value, the total number of orbitals is n2.
  • Angular Momentum (Secondary, Azimunthal) l = 0,..., n-1 Quantum Number

(B) n = 2

  • The n = 2 states begin to fill up as we move to larger atoms, adding electrons one at a time.
  • Because there are four different values for (l, m), each with two allowed spin states, the n = 2 states can hold up to eight electrons.
  • The n = 2 shell includes all states with a quantum number of n = 2.

Therefore, Quantum numbers are:

  • (A) n = 1 ⇒ n -1
  • (B) n = 2 ⇒ n = 2

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