The X-ray spectrum for a typical metal is shown in Figure 31-22. Find the approx

Question

The X-ray spectrum for a typical metal is shown in Figure 31-22. Find the approximate wavelength of K X-rays emitted by chromium. (Hint: An electron in the M shell is shielded from the nucleus by the single electron in the K shell, plus all the electrons in the L shell.)

Z=atomic number of chromium (24)

for Ek  n1=1

for Em  n1=3

Used E= -13.6eV(Z-1)2/n12

Found Ek , Em  Used these two values to find E.  Converted E to J. Then plugged everything in to this formula =hc/E

Came up with -1.94e-16 and that was wrong. 

Where did I go wrong?

Explanation / Answer

atomic number of chromium Z = 24 plank's constant h = 6.63*10-34 J-s speed of light c = 3*108 m/s if an electron drops from n = 3 level to the K-shell (n = 1) , the resulting peak is called the K line. energy of a K -shell (n = 1) electron ,             EK =  -13.6eV(Z-1)2/n2                   = -13.6eV(24-1)2/(1)2                   = -7194.40 eV energy of a m -shell (n = 3) electron ,             Em =  -13.6eV(Z-1)2/n2                   = -13.6eV(24-1)2/(3)2                   = -799.37 eV change in energy , E = Ek - Em                                     = -7194.40 eV - (-799.37 eV)                                     = -6395.03 eV                 (since , 1 eV = 1.6*10-19 J)                                     = -(6395.03*1.6*10-19) J                                     = -10232.048*10-19 J wavelength corresponding to E ,                    = hc / IEI                       = {(6.63*10-34 J-s)(3*108 m/s)} / I(-10232.048*10-19 J)I                       = 1.943*10-10 m                       = 0.1943*10-9 m                       = 0.1943 nm                                       = -7194.40 eV energy of a m -shell (n = 3) electron ,             Em =  -13.6eV(Z-1)2/n2                   = -13.6eV(24-1)2/(3)2                   = -799.37 eV change in energy , E = Ek - Em                                     = -7194.40 eV - (-799.37 eV)                                     = -6395.03 eV                 (since , 1 eV = 1.6*10-19 J)                                     = -(6395.03*1.6*10-19) J                                     = -10232.048*10-19 J wavelength corresponding to E ,                    = hc / IEI                       = {(6.63*10-34 J-s)(3*108 m/s)} / I(-10232.048*10-19 J)I                       = 1.943*10-10 m                       = 0.1943*10-9 m                       = 0.1943 nm                     energy of a m -shell (n = 3) electron ,             Em =  -13.6eV(Z-1)2/n2                   = -13.6eV(24-1)2/(3)2                   = -799.37 eV change in energy , E = Ek - Em                                     = -7194.40 eV - (-799.37 eV)                                     = -6395.03 eV                 (since , 1 eV = 1.6*10-19 J)                                     = -(6395.03*1.6*10-19) J                                     = -10232.048*10-19 J wavelength corresponding to E ,                    = hc / IEI                       = {(6.63*10-34 J-s)(3*108 m/s)} / I(-10232.048*10-19 J)I                       = 1.943*10-10 m                       = 0.1943*10-9 m                       = 0.1943 nm                                                         = -7194.40 eV - (-799.37 eV)                                     = -6395.03 eV                 (since , 1 eV = 1.6*10-19 J)                                     = -(6395.03*1.6*10-19) J                                     = -10232.048*10-19 J wavelength corresponding to E ,                    = hc / IEI                       = {(6.63*10-34 J-s)(3*108 m/s)} / I(-10232.048*10-19 J)I                       = 1.943*10-10 m                       = 0.1943*10-9 m                       = 0.1943 nm                    

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