The energy of an electron is defined by E = -2.178 times 10^ -18 text J (frac Z^ 2 n^ 2 ). Calculate the wavelength of light necessary to excite an electron in a hydrogen atom from the ground state (n=1) to the first excited state (n=2).

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EEJ MAIN Chemistry QUESTION #7170

Question 1

The energy of an electron is defined by $E = -2.178 \times 10^{-18} \text{ J} (\frac{Z^{2}}{n^{2}})$. Calculate the wavelength of light necessary to excite an electron in a hydrogen atom from the ground state ($n=1$) to the first excited state ($n=2$).

$1.214 \times 10^{-7} \text{ m}$✔️
$2.816 \times 10^{-7} \text{ m}$
$6.500 \times 10^{-7} \text{ m}$
$8.500 \times 10^{-7} \text{ m}$

Correct Answer Explanation

To find the wavelength, we first calculate the energy difference:

$\Delta E = E_{2} - E_{1} = -2.178 \times 10^{-18} (\frac{1}{2^{2}} - \frac{1}{1^{2}}) \text{ J}$
$\Delta E = 2.178 \times 10^{-18} \times \frac{3}{4} = 1.6335 \times 10^{-18} \text{ J}$
Using $\lambda = \frac{hc}{\Delta E}$:
$\lambda = \frac{6.62 \times 10^{-34} \times 3 \times 10^{8}}{1.6335 \times 10^{-18}} \approx 1.214 \times 10^{-7} \text{ m}$

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