Energy of nth  state of hydrogen is given byEn​=n2−13.6​eV Energy of first excited state (n=2)of hydrogen, E1​=4−13.6​eV=−3.4eV This relation holds true when the refrence point energy is zero.Usually the refrence point energy is the energy of the atom when the electron is widely separated from the proton.In the given question, the potential energy of the atom is taken to be 10eV when the electron is widely separated from the proton so here our reference point energy is 10eV. Earlier The energy of first excited state was −3.4eV when the reference point had zero energy but now as the refrence point has shifted so The energy of the first excited state will also shift by the corresponding amount.Thus,E1′​=−3.4eV−10eV=−13.4eV We still write En​=E1​/n2 , or rn​=a0​n2 because these formulas are independent of the refrence point enegy.