The line spectrum for element X includes a band of green light of wavelength 522 nm. This band corresponds to what energy transition within an atom of element X? Let Planck’s constant h = 4.136 × 10−15 eV ∙ s, and the speed of light c = 3.00 × 108 m/s.

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Answer 1 · 2017-05-25T20:42:18

decrease of #2.38# #"e V"#

Let's substitute the value of #h# into the Planck equation #E = h f#:

#Rightarrow E = (4.136 times 10^(- 15)# #"e V"# #cdot# #"s")# #times f#

Then, let's substitute the definition of #f#, #f = frac(c)(lambda)#, into the above equation:

#Rightarrow E = (4.136 times 10^(- 15)# #"e V"# #cdot# #"s")# #times frac(c)(lambda)#

Let's substitute the values of #c# and #lambda# into the equation:

#Rightarrow E = (4.136 times 10^(- 15)# #"e V"# #cdot# #"s")# #times frac(3.00 times 10^(8) " m s"^(- 1))(522 " nm")#

#Rightarrow E = (4.136 times 10^(- 15)# #"e V"# #cdot# #"s")# #times frac(3.00 times 10^(8) " m s"^(- 1))(5.22 times 10^(- 7) " m")#

#Rightarrow E = frac(1.2408 times 10^(- 6) " e V" cdot "m")(5.22 times 10^(- 7) " m")#

#Rightarrow E = 2.337# #"e V"#

#therefore E = 2.38# #"e V"#

Therefore, this band corresponds to a decrease of #2.38# #"e V"#.