Final answer:
The energy of an electron with n = 6 in a hydrogen atom can be calculated using the Bohr model formula. After calculating, the result is -6.05 × 10^{-20} J, which does not match any provided options, potentially due to a typo in the exponent. The closest match considering the exponent typo would be -2.18 × 10^{-18} J.
Step-by-step explanation:
Using the Bohr model, we can determine the energy of an electron with the principal quantum number n in a hydrogen atom with the formula:
E_n = - rac{2.18 × 10^{-18}}{n^2} ext{Joules}
For an electron with n = 6:
E_6 = - rac{2.18 × 10^{-18}}{6^2} ext{Joules}
E_6 = - rac{2.18 × 10^{-18}}{36}
E_6 = - rac{2.18 × 10^{-18}}{36}
E_6 = -0.0605 × 10^{-18} ext{Joules}
E_6 = -6.05 × 10^{-20} ext{Joules}
Therefore, the energy of the electron with n = 6 in a hydrogen atom is -6.05 × 10^{-20} J, which is not exactly matching any of the options provided in the question. It's possible there is a discrepancy in the values or units provided in the question. The closest answer to this calculated value, if we consider the exponent as -18 instead of -20 by assuming a typo, would be option a) –2.18 × 10²¹¸ J.