What is the energy of an electron in the first energy level of hydrogen? A -1.089times 10^-18J B -2.178times 10^-18J C -4.356times 10^-18J D -5.445times 10^-19J

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What is the energy of an electron in the first energy level of hydrogen? A -1.089times 10^-18J B -2.178times 10^-18J C -4.356times 10^-18J D -5.445times 10^-19J

Answer 1

The energy of an electron in the first energy level of hydrogen is \(\boxed{-2.178 \times 10^{-18} \mathrm{~J}}\) (Option B).

Answer 2

The energy levels of an electron in a hydrogen atom can be calculated using the formula for the energy of an electron in a given orbit of a hydrogen atom, which is given by:\[E_n = \frac{-13.6 \text{ eV}}{n^2}\]where \(E_n\) is the energy of the electron at the nth energy level, and \(n\) is the principal quantum number of the energy level. The energy level of the first orbit (ground state) is when \(n = 1\).First, we need to calculate the energy in electron volts (eV) and then convert it to joules (J) since the options are given in joules. The conversion factor from electron volts to joules is \(1 \text{ eV} = 1.602 \times 10^{-19} \text{ J}\).For the first energy level (\(n = 1\)):\[E_1 = \frac{-13.6 \text{ eV}}{1^2} = -13.6 \text{ eV}\]Now, convert this energy to joules:\[E_1 (\text{in joules}) = -13.6 \text{ eV} \times 1.602 \times 10^{-19} \frac{\text{J}}{\text{eV}}\]\[E_1 (\text{in joules}) = -13.6 \times 1.602 \times 10^{-19} \text{ J}\]\[E_1 (\text{in joules}) = -2.17872 \times 10^{-18} \text{ J}\]The value is rounded to the significant figures based on the given options:\[E_1 (\text{in joules}) \approx -2.178 \times 10^{-18} \text{ J}\]

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What is the energy of an electron in the first energy level of hydrogen? A -1.089times 10^-18J B -2.178times 10^-18J C -4.356times 10^-18J D -5.445times 10^-19J

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