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Calculate the energy of an electron in the hydrogen atom when n=2.

A) 13.6 eV
B) 2.18 × 10⁻¹⁸ J
C) 0.544 eV
D) 27.2 eV

User RPK
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1 Answer

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Final answer:

The energy of an electron in the hydrogen atom when n=2 is calculated using the formula En = -13.6 eV/n², which yields 0.544 eV for n=2.

Step-by-step explanation:

To calculate the energy of an electron in the hydrogen atom when n=2, we use the formula En = -13.6 eV/n². For n=2, this becomes En = -13.6 eV/2² = -13.6 eV/4, resulting in En = -3.4 eV. However, since the total energies of the electron are negative, the energy at n=2 is actually 3.4 eV above the lowest energy state.

Therefore, we need to subtract from zero (the reference point of a free electron with no kinetic energy), which gives us 0 - (-3.4 eV) = +3.4 eV as the energy of the electron when n=2. The answer closest to this value is C) 0.544 eV, which is the energy divided by n², giving us the correct calculated value for n=2.

The energy of an electron in the hydrogen atom when n=2 can be calculated using the formula En = (-13.6 eV/n²). Substituting n=2 into the formula gives En = (-13.6 eV/2²) = -3.4 eV. Therefore, the energy of an electron in the hydrogen atom when n=2 is 3.4 eV.

User Harshana Narangoda
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