Suppose that a hydrogen atom inthe ground state absorbs a photon of wavelength18

Question

Suppose that a hydrogen atom inthe ground state absorbs a photon of wavelength18.6nm. If theatom is ionized, what will be the kinetic energy of the electronwhen it gets far away from its atom of origin? The value of¯h is1.05457× 1034 J · s ; the speed of light is 2.99799 × 108m/s ; the value of his 6.62607 × 1034 J· s ; theRydberg constant for hydrogen is 1.09735 × 107m1 ;the Bohr radius is 5.29177 × 1011 m; and the ground state energy for hydrogen13.6057eV. 1 eV =1.60218× 1019 J .Answer in units of eV

Explanation / Answer

wavelength = 18.6 nm = 18.6 * 10 ^ -9 m energy of the photon E = hc / where h = planck's constant = 6.625 * 10 ^ -34 J s            c= speed of light = 3 * 10 ^ 8 m / s substitue values we get E = 1.0685 * 10 ^ -17 J                                       = 106.85* 10 ^ -19 J                                       = 106.85 * 10 ^ -19 / ( 1.6 * 10 ^ -19 ) eV                                       = 66.78 eV we know ionozation energy of the electron in ground stateis = 13.6 eV So,  kinetic energy of the electron when it gets faraway from its atom of origin = 66.78 eV - 13.6 eV                                                                                                                      = 53.18 eV

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