The work function (#Φ#) for a metal is #5.90*10^-19 J#. What is the longest wavelength of electromagnetic radiation that can eject an electron from the surface of a piece of the metal?

1 Answer
1s2s2p
Feb 28, 2018

#lambda=3.37*10^-7m#

Explanation:

Einstein's photoelectric equation is:
#hf=Phi+1/2mv_max^2#, where:

  • #h# = Planck's constant (#6.63*10^-34Js#)
  • #f# = frequency (#m#)
  • #Phi# = work function (#J#)
  • #m# = mass of the charge-carrier (#kg#)
  • #v_max# = maximum velocity (#ms^-1#)

However, #f=c/lambda#, where:

  • #c# = speed of light (#~3.00*10^8ms^-1#)
  • #lambda# = wavelength (#m#)

#(hc)/lambda=Phi+1/2mv_max^2#

#lambda=(hc)/(Phi+1/2mv_max^2)#

#lambda# is a maximum when #Phi+1/2mv_max^2# is a minimum, which is when #1/2mv_max^2=0#

#lambda=(hc)/Phi=((6.63*10^-34)(3.00*10^8))/(5.90*10^-19)=3.37*10^-7m#

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