Please show all the steps!!! Thank you ! If a photon with sufficient energy inte

Question

Please show all the steps!!! Thank you !

If a photon with sufficient energy interacts with a bound electron, it will be set free. The kinetic energy of such a photoelectron will be what is left over after paying the price in energy to break the tether. So: E_photon = |E_binding |+|E_ kineticI or: E_ available= I E_tetherl+|E_left for speed| Assuming that the Bohr model is valid, what is the kinetic energy of a photoelectron liberated by a photon with a the given wavelength from a state with given Z and n? If the available energy is insufficient to break the tether, enter 0. Lambda =100 nanometers from a state with Z=2 and n = 4 lambda =240 nanometers from a state with Z=1 and n = 4 X in Joules. E_photon = hv h = planck's constant = 6.626e - 34 [Js] lambda * v = c = 2.9979e + 8 [m/s] 1 [eV] = 1.602e - 19 [Joule]

Explanation / Answer

for wavelength = 100 nm
E = h*c/wavelength
   = (6.626*10^-34)*(3*10^8) / (100*10^-9)
   =1.9878*10^-18 J

for Z=2 and n=4 energy binding,
E bind = 13.6*Z^2 *(1/n^2)
             = 13.6*2^2/4^2
             = 3.4 eV
             = 3.4 * 1.602*10^-19 J
             =5.4468*10^-19 J

Knetic energy =1.9878*10^-18 - 5.4468*10^-19 = 1.44*10^-18 J

for wavelength = 240 nm
E = h*c/wavelength
   = (6.626*10^-34)*(3*10^8) / (240*10^-9)
   =8.2825*10^-19 J

for Z=1 and n=4 energy binding,
E bind = 13.6*Z^2 *(1/n^2)
             = 13.6*1^2/4^2
             = 0.85 eV
             = 0.85 * 1.602*10^-19 J
             =1.3617*10^-19 J

Knetic energy =8.2825*10^-19   - 1.3617*10^-19 = 6.92*10^-19 J

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