Question

Using Bohr's equation for the energy levels of the electron in a Hydrogen atom, determine the energy of an electron in $n=4$.

• A. $-5.45\times {10}^{-19}$J
• B. $-1.84\times {10}^{-29}$J
• C. $-1.365\times {10}^{-19}$J
• D. $1.84\times {10}^{-29}$J

Answer 1

The correct option is C $-1.365\times {10}^{-19}$J

Energy in Bohr's Model (For Hydrogen)

$E_n=-\frac{e^2}{8\pi {\in }_0{n}^2{a}_0}$

$E_n=-\frac{E_1}{n^2}$

$E_n=-\frac{13.6}{n^2}ev$

$E_4=-\frac{13.6}{16}\times 1.6\times {10}^{-19}J$

$E_4=-1.36\times {10}^{-19}J$