Calculate the energy, in joules, required to excite a hydrogen atom by causing an electronic transition from the n = 1 to the n = 4 principal energy level. Recall that the energy levels of the H atom are given by E_n = -2.18 × 10^-18 J(1/n²). A) 2.07 × 10^-29 J B) 2.19 × 10⁵ J C) 2.04 × 10^-18 J D) 3.27 × 10^-17 J E) 2.25 × 10^-18 J

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The energy required for the transition is calculated using the formula for the energy levels of a hydrogen atom: $E = -2.18 \times 10^{-18} J \left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$, where $n_f$ is the final energy level and $n_i$ is the initial energy level. Substituting $n_f = 4$ and $n_i = 1$, we get $E = -2.18 \times 10^{-18} J \left(\frac{1}{4^2} - \frac{1}{1^2}\right) = -2.18 \times 10^{-18} J \left(\frac{1}{16} - 1\right) = -2.18 \times 10^{-18} J \left(-\frac{15}{16}\right) = 2.04 \times 10^{-18} J$.

Calculate the Energy, in Joules, Required to Excite a Hydrogen