If the energy of an electron within the boron atom was calculated as –6.0556 x 10^-18 J, at what energy level would it reside?

• A. 2
• B. 3
• C. 4
• D. 5

Answer: (B)

Verified step by step guidance

1. Understand that the energy of an electron in an atom is given by the formula: $E=-\frac{R_H}{z^2}$, where RH is the Rydberg constant (2.18 x 10^-18 J), z is the atomic number, and n is the principal quantum number or energy level.
2. Identify the atomic number of boron, which is $5$.
3. Rearrange the formula to solve for $n$: $n=\sqrt{\frac{R_H}{z^2}}$.
4. Substitute the given energy value $-6.0556\times {10}^{-}$ J, the Rydberg constant, and the atomic number of boron into the rearranged formula.
5. Calculate the value of $n$ to determine the energy level at which the electron resides.