Question:

An electron is located in the n=3 energy level of a hydrogen atom. Calculate the energy of the electron in eV.

Given:

• Planck's constant (h) = 6.626 x 10^-34 J·s
• Speed of light (c) = 3.00 x 10^8 m/s
• Charge of an electron (e) = 1.602 x 10^-19 C
• Permittivity of free space (ε0) = 8.85 x 10^-12 C^2/N·m^2
• n=3 (quantum number)

Answer: To calculate the energy of an electron in a particular energy level, we can use the formula for the energy of an electron in the nth energy level of a hydrogen atom:

E = - (13.6 eV) / n^2

Where E is the energy of the electron, and n is the quantum number representing the energy level.

Plugging in the value n=3: E = - (13.6 eV) / 3^2 E = - (13.6 eV) / 9 E = -1.5111 eV

Therefore, the energy of the electron in the n=3 energy level of a hydrogen atom is -1.5111 eV.