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
Truong-Son N.
Mar 1, 2018

Well, since we know that

#phi = 5.90 xx 10^(-19) "J" = hnu_0#,

with #nu_0# being the threshold frequency and #h# being Planck's constant, then the threshold (i.e. MINIMUM) frequency required to ionize the metal is:

#nu_0 = (5.90 xx 10^(-19) "J")/(6.626 xx 10^(-34) "J"cdot"s") = 8.90 xx 10^14 "s"^-1#

The MAXIMUM wavelength this corresponds to is

#color(blue)(lambda_0) = c/nu_0 = (2.998 xx 10^8 "m/s")/(8.90 xx 10^14 "s"^-1) = 3.37 xx 10^(-7) "m"#

#=# #color(blue)("337 nm")#

Based on this, is green light going to work?

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