Question:
What is the maximum value of the wavelength of light that will ionize the hydrogen atom?
Take the energy of the ground state of the hydrogen atom to be $-0.99946650834 R_\infty h c \,$, where $R_\infty$ is the Rydberg constant and $c$ is the speed of light.
Solution:
Recall the potential energy of an item in a gravitational field is define to have 0 potential energy if and only if it is at infinitely far. I guess the same idea apply here when we say the energy of the ground state of the hydrogen atom is a negative number.
So we need a photon with energy just enough of make the overall energy 0.
A photon has energy $ E = hf = \frac{hc}{\lambda} $. Therefore we have $ \lambda = \frac{hc}{0.99R_\infty hc} = 9.11 \times 10^-{8} $, or 91 nanometers.
What is the maximum value of the wavelength of light that will ionize the hydrogen atom?
Take the energy of the ground state of the hydrogen atom to be $-0.99946650834 R_\infty h c \,$, where $R_\infty$ is the Rydberg constant and $c$ is the speed of light.
Solution:
Recall the potential energy of an item in a gravitational field is define to have 0 potential energy if and only if it is at infinitely far. I guess the same idea apply here when we say the energy of the ground state of the hydrogen atom is a negative number.
So we need a photon with energy just enough of make the overall energy 0.
A photon has energy $ E = hf = \frac{hc}{\lambda} $. Therefore we have $ \lambda = \frac{hc}{0.99R_\infty hc} = 9.11 \times 10^-{8} $, or 91 nanometers.
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