QNEET-2024-Ch-20: NEET 2024 Chemistry - Class 11 NEET-2024-Ch-20 Solution: The energy of an electron in the ground state (n=1) for…

The energy levels of an electron in a hydrogen-like ion (an atom or ion with only one electron) can be quantified using the formula: E n = _ Z 2 _ 13.6  eV n 2 where: E n is the energy of the electron in the nth energy level, Z is the atomic number (number of protons) of the ion, 13.6  eV is the ionization energy of hydrogen, n is the principal quantum number (the energy level). Since we need to compare this across different ions in different energy states, let's plug in some numbers: For He + (Helium ion): Z = 2 (as helium has 2 protons) n = 1 for ground state E 1 = _ ( 2 ) 2 _ 13.6  eV 1 2 = _ 4 _ 13.6  eV = _ 54.4  eV However, the problem gives the energy in joules, and it's given a constant x . So, x = 54.4  eV (converted to joules as needed). Next, for the Be 3 + ion: Z = 4 (as beryllium has 4 protons) n = 2 E 2 = _ ( 4 ) 2 _ 13.6  eV 2 2 = _ 16 _ 13.6  eV 4 = _ 54.4  eV Since initially x = 54.4  eV (or its equivalent in joules) for He +  at  n = 1 , and now we have the same energy for Be 3 +  at  n = 2 , the energy level in joules would also equate to x , just at a different energy state and ion. So, the answer is: Option A: _ x .