Question

Calculate the ionization potential energy
of an electron in an excited state, if the electron was traveling at energy n=1

Answer 1

Answer on Question #77989 – Chemistry – Other

Calculate the ionization potential energy of an electron in an excited state, if the electron was travelling at energy $n=1$

Solution:

The Rydberg Expression is given by:

$$\frac {1}{\lambda} = R \left[ \frac {1}{n _ {1} ^ {2}} - \frac {1}{n _ {2} ^ {2}} \right]$$

$\lambda$ is the wavelength of the emission line

$n_1$ is the principle quantum number of the lower energy level

$n_2$ is the principle quantum number of the higher energy level

R is the Rydberg Constant $1.097 \times 10^{7} \, \text{m}^{-1}$

For example, the energy levels converge and coalesce:

Hydrogen

Energy Levels for the Hydrogen Atom

At higher and higher values of $n_2$ the term $\frac{1}{n_2^2}$ tends to zero. Effectively $n_2 = \infty$ and the electron has left the atom, forming an ion.

The Rydberg Expression refers to emission where an electron falls from a higher energy level to a lower one, emitting a photon.