MHTCET 16 Apr 2026 Shift 1 Paper

Concept:The energy of an electron in a hydrogen atom is quantized, meaning it can only occupy specific energy levels determined by the principal quantum number $n$.Explanation:For a hydrogen atom, the energy of an electron in the $n$th stationary state is given by the Rydberg formula:$$E_n = -\frac{2.18 \times 10^{-18}}{n^2} \mathrm{~J}$$Here, $n$ is the principal quantum number, and the negative sign indicates a bound state.For $n = 2$, substitute this value into the formula:$$E_2 = -\frac{2.18 \times 10^{-18}}{2^2}$$Since $2^2 = 4$, the expression becomes:$$E_2 = -\frac{2.18 \times 10^{-18}}{4}$$Perform the division to get:$$E_2 = -5.45 \times 10^{-19} \mathrm{~J}$$The negative sign confirms that the electron is bound to the nucleus, and energy must be supplied to ionize the atom.Comparing with the given options, this value matches option A exactly.Answer:The energy of the electron in the $n = 2$ stationary state is $-5.45 \times 10^{-19} \mathrm{~J}$.Therefore, the correct option is A.