The quantum numbers of four states for an electron in an excited hydrogen atom are given below: I. n=4 ; l=0 ; m_l=0 ; s=+ 1 2 II. n=3 ; l=2 ; m_l=-1 ; s=- 1 2 III. n=3 ; l=1 ; m_l=1 ; s=+ 1 2 IV. n=3 ; l=0 ; m_l=0 ; s=- 1 2 The correct decreasing order of energy of these states is:

Step-by-step solution

For a single-electron species like the hydrogen atom, the energy of an electron depends only on the principal quantum number ( n ) and is independent of the azimuthal quantum number ( l ). The subshells with the same principal quantum number are degenerate (have equal energy). State I represents the 4s orbital ( n=4 ). State II represents the 3d orbital ( n=3 ). State III represents the 3p orbital ( n=3 ). State IV represents the 3s orbital ( n=3 ). Since energy increases with an increase in n , the 4s orbital has