MHTCET 19 Apr 2026 Shift 2 Paper

Concept:The energy of an electron in a hydrogen atom depends on the principal quantum number $n$ and is given by the Bohr model formula $E_n = -\dfrac{13.6}{n^2}\ \text{eV}$.Explanation:The ground state corresponds to $n = 1$, so its energy is:$$E_1 = -\frac{13.6}{1^2} = -13.6\ \text{eV}$$The next higher state corresponds to $n = 2$, so its energy is:$$E_2 = -\frac{13.6}{2^2} = -\frac{13.6}{4} = -3.4\ \text{eV}$$The energy required to excite the atom from the ground state to this higher state is the difference between the two energy levels:$$\Delta E = E_2 - E_1$$$$\Delta E = (-3.4) - (-13.6) = 10.2\ \text{eV}$$Since this is a positive value, the atom must absorb $10.2\ \text{eV}$ of energy during the transition.Answer:The energy required is nearly $10.2\ \text{eV}$, so the correct option is C.