Question

The maximum energy that a hydrogen atom can have is 0 J, at which point the electron is essentially removed from the atom; thus ionization occurs. How much energy ( in joules ) does it take to ionize a hydrogen atom? What wavelength to ionize a hydrogen?

Answer 1

The ground level of the hydrogen atom is at `-13.6 eV` or `-2.178×10^-18 J` which is the energy needed to take the electron from the ground level to the one at zero energy.

Using the relationship: `E=h*nu` you can find the frequency `nu` needed;
`nu=(2.178×10^-18)/(6.626×10^-34)=3.285×10^15 Hz` where `h` is Plank's constant.

but `c=lambda*nu` where `lambda` is the wavelength and `c` is the speed of light (`3×10^8 m/s`)..
So you get:
`lambda=c/(nu)=(3×10^8)/(3.285×10^15)=91.3nm`

Please check my maths!