In the Bohr model of the hydrogen atom, what is the energy of the electron in th

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Question: In the Bohr model of the hydrogen atom, what is the energy of the electron in the n=2 level?

Options:

Correct Answer: -3.4 eV

Solution:

The energy of an electron in the nth level of hydrogen is given by E_n = -13.6 eV/n². For n=2, E_2 = -13.6 eV/2² = -3.4 eV.

In the Bohr model of the hydrogen atom, what is the energy of the electron in the n=2 level?

In the Bohr model of the hydrogen atom, what is the energy of the electron in the n=2 level?

Step 1: Understand that we are using the Bohr model for the hydrogen atom.
Step 2: Know the formula for the energy of an electron in the nth level: E_n = -13.6 eV/n².
Step 3: Identify the value of n we are interested in, which is n=2.
Step 4: Substitute n=2 into the formula: E_2 = -13.6 eV/(2²).
Step 5: Calculate 2², which is 4.
Step 6: Now substitute this value back into the equation: E_2 = -13.6 eV/4.
Step 7: Perform the division: -13.6 eV divided by 4 equals -3.4 eV.
Step 8: Conclude that the energy of the electron in the n=2 level is -3.4 eV.

Bohr Model of the Hydrogen Atom – The Bohr model describes the quantized energy levels of electrons in a hydrogen atom, where the energy of an electron is inversely proportional to the square of its principal quantum number (n).
Energy Levels – The energy levels of an electron in a hydrogen atom are calculated using the formula E_n = -13.6 eV/n², which indicates that energy becomes less negative (higher) as n increases.