What wavelength of light contains enough energy in a single photon to ionize a hydrogen atom?

NetherCraft 0

wavelenght in “nm”

1 Answer

  • The ionization energy of hydrogen is 1312 kJ/mol. The energy required to ionize a single hydrogen atom is this quantity divided by Avagadro’s number (the number of particles in a mole):

    (1.312*10^6 J/mol)/(6.022*10^23 atoms/mol) =

    2.179*10^-18 J/atom

    The energy of a photon is related to its wavelength by:

    E = h*c/wavelength

    where c is the speed of light in a vacuum = 2.998*10^8 m/s

    h is Planck’s constant = 6.626*10^-34 (kg*m^2)/s

    Solving for the wavelength of a photon that has enough energy to ionize hydrogen:

    wavelength = (2.998*10^8 m/s)*(6.626*10^-34 (kg*m^2)/s)/(2.179*10^-18 J)

    wavelength = 9.118*10^-8 m = 91.18 nm

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