A photon of wavelength 80 nm is absorbed by the electron in the ground-state level of the hydrogen atom.Is this enough energy to ionize the atom? If so calculate the kinetic energy of the free electron.
A)No,ionization does not occur.
B)Yes,1.9 eV
C)Yes,12 eV
D)Yes,29 eV
E)Yes,19 eV

Question

Quizplus · Accepted Answer

The energy required to ionize a hydrogen atom from its ground state is 13.6 eV. The energy of a photon is given by $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{m}^2 \, \text{kg} / \text{s}$), $c$ is the speed of light ($3.00 \times 10^8 \, \text{m/s}$), and $\lambda$ is the wavelength of the photon. Substituting the given wavelength of 80 nm ($80 \times 10^{-9} \, \text{m}$), we find the photon's energy to be approximately 15.5 eV. Since this is greater than 13.6 eV, ionization occurs. The kinetic energy of the ejected electron is the difference between the photon's energy and the ionization energy, which is $15.5 \, \text{eV} - 13.6 \, \text{eV} = 1.9 \, \text{eV}$.

A Photon of Wavelength 80 Nm Is Absorbed by the Electron