Question

The first ionization energy, ????, of a carbon atom is 1.81 aJ. What is the wavelength of light, in nanometers, that is just sufficient to ionize a carbon atom?

Answer 1

Answer:

109.8 nm

Explanation:

The first ionization energy of a hydrogen atom is,

$E=1.81aJ\\E=1.81\times 10^{-18} J$

And Plank's constant, $h=6.626\times 10^{-34}Js$

And the speed is, $c=3\times 10^{8}m/s$

Now the formula for energy will be,

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

Put all the variable after rearranging for lambda.

$\lambda=\frac{6.626\times 10^{-34}Js(3\times 10^{8}m/s)}{1.81\times 10^{-18} J} \\\lambda=10.98\times10^{-8}m\\\lambda=109.8\times 10^{-9}m\\\lambda=109.8 nm$

Therefore the wavelength of light is 109.8 nm to ionize a carbon atom .