# Quantum Mechanics 1 | Week 11

Session: JAN-APR 2024

Course name: Quantum Mechanics I

#### Q1. The ground state energy of the Hydrogen atom is given as E₁ = -R, where R = 13.6 eV is the Rydberg constant. If the atom makes a transition from the excited state n = 3 to the state n = 2, then the radiation emitted would be ______________eV. (Write upto two decimal places.)

Q2. The allowed angular momentum j when we add two particles with angular momentum j15/2 and j2 = 3/2 are
a) 0, 1, 2, 3, 4
b) 1/2,3/2,5/2
c) 1,2,3,4
d) 7/2,5/2,3/2

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Q3. The matrix element of z between 4F and 4D hydrogen states is given by
2 <4F, m = 2/2/4D, m = 2) = -300
where ao is the Bohr radius. (4F, m = 3|y|4D, m = 2) will be

a) i√2/3a0
b) -ia0
c) i√3/2a0
d) ia0

Q4. The product of the position vector component zy in terms of spherical rank two tensor T be 2) will

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Q5. The maximum degeneracy of states when we add angular momentum j₁ = 4 and j₂ = 2 is
a) 2
b) 4
c) 9
d) 5

Q6. Consider a state vector
The possible measurements of square of angular momentum operator L2 on the eigenstate 2, -1) is ___________ h². (Answer should be an integer)

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Q7. Two atoms with angular momentum J₁ = 2 and J2 1 are coupled and are described by Hamiltonian H = € J1 J2, where € > 0. If the Hamiltonian acts on J, M) state, then the energy eigenvalues corresponding to the possible values of total angular momentum J will be
a) -3€h², -€h², 2€h²
b) €h², -3€h², 2€h²
c) 2€h², €h², 3€h²
d) -€h², 2€h², 3€h²

Q8. The Clebsch-Gordan coefficient (m₁=j1, m₂-12+3|j 11+12. m) will be non-zero if
a) m = j1+j2 – 3
b) m = j1 + j2
c) m = j1 – j2 + 2
d) m = j2 – 1 – j1.

Answer: c) m = j1 – j2 + 2

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Q9. The parity operator P anti-commutes with the orbital angular momentum operator L.
a) True
b) False

Q10.