An excited electron falls from n = 4 to n = 2. a. calculate the energy change in joules associated with this transition.

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20-12-2022
Mathematics

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An excited electron falls from n = 4 to n = 2. a. calculate the energy change in joules associated with this transition.

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contexto1019 contexto1019 · Answer 1 · 2022-12-22T11:49:13-05:00

To calculate the energy change associated with an electron transitioning from the n = 4 energy level to the n = 2 energy level, we can use the equation for the energy of an electron in an atom, which is given by:

E_n = -13.6 eV * (1/n^2)

Where E_n is the energy of the electron in the nth energy level, and eV is the unit of energy called the electronvolt.

Substituting the values of n = 4 and n = 2 into this equation gives us:

E_2 = -13.6 eV * (1/2^2) = -13.6 eV * (1/4) = -3.4 eV
E_4 = -13.6 eV * (1/4^2) = -13.6 eV * (1/16) = -0.85 eV

The energy change associated with the transition from n = 4 to n = 2 is given by

E_2 - E_4 = (-3.4 eV) - (-0.85 eV) = -2.55 eV.

To convert this energy change from electronvolts to joules, we can use the fact that 1 eV is equal to 1.602176634 x 10^-19 joules.

Multiplying -2.55 eV by this conversion factor gives us an energy change of -2.55 eV * 1.602176634 x 10^-19 joules/eV = -4.13 x 10^-18 joules.

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