Rydberg Equation Maths

Most questions you will get would be something along the lines of:

• Find the wavelength of the electromagnetic wave released when an electron moves from n = 5 to n = 2.
(1)
\begin{align} \frac{1}{\lambda} = R_h \bigg(\frac{1}{{n_f}^2} - \frac{1}{{n_i}^2}\bigg) \end{align}
(2)
\begin{align} \frac{1}{\lambda} = R_h \bigg(\frac{1}{{2}^2} - \frac{1}{{5}^2}\bigg) \end{align}
(3)
\begin{align} \frac{1}{\lambda} = 2.303229252 \times 10^{6} \end{align}
(4)
\begin{align} \therefore \lambda = 434.17 nm \end{align}

They could also ask slight variations such as:

• Find the frequency of the electromagnetic wave released when an electron moves from n = 5 to n = 2.
(5)
\begin{align} f = \frac{c}{\lambda} \end{align}
(6)
\begin{align} \therefore f = \frac{c}{4.3417 \times 10^{-7}} or f = c \times 2.303229252 \times 10^{6} \end{align}
(7)
\begin{align} f = 6.90490759 \times 10^{14} Hz \end{align}
• Find the energy of the electromagnetic wave released when an electron moves from n = 5 to n = 2.
(8)
\begin{align} E = hf | E = h \frac{c}{\lambda} \end{align}
(9)
\begin{align} \therefore E = h \times 6.90490759 \times 10^{14} | E = h \times \frac{c}{4.3417 \times 10^{-7}} \end{align}
(10)
\begin{align} \therefore E = 4.57524×10^-19 J|2.85564 eV \end{align}
page revision: 1, last edited: 29 Oct 2011 12:45