Question

The first ionization energy, ????, of a hydrogen atom is 2.18 aJ. What is the wavelength of light, in nanometers, that is just sufficient to ionize a hydrogen atom? V

Answer 1

Answer:

Wavelength of light is 91.2 nm.

Explanation:

The first ionization energy of a hydrogen atom is,

$E=2.18aJ\\E=2.18\times10^{-18}J$

And Plank's constant, $h=6.626\times10^{-34}Js$

And the speed is, $c=3\times10^{8}m/s$

Now the formula for energy will be,

$E=\frac{hc}{\lambda}$

Put all the variable after rearranging for lambda.

$\lambda=\frac{6.626\times10^{-34}Js(3\times10^{8}m/s)}{2.18\times10^{-18}J} \\\lambda=9.12\times10^{-8}m\\\lambda=91.2\times10^{-9}m\\\lambda=91.2nm$

Therefore the wavelength of light is 91.2 nm.