In a sample of excited hydrogen atoms electrons make transition from n = 3 to n = 1 and emitted photons strike on a metal of work function 6.08 eV. The maximum kinetic energy of the ejected electron in the process will be?

4 eV

6 eV

2 eV

8 eV

4 eV

6 eV

2 eV

8 eV
1 Answer
Explanation:
The idea here is that in order for an electron to be ejected from the surface of the metal, the energy of the incoming photon must exceed the work function of the metal.
So you can say that you have
#color(blue)(ul(color(black)("K"_ "E" = E_"photon"  W)))" " " "color(darkorange)(("*"))#
Here
#"K"_"E"# is the kinetic energy of the ejected electron#E_"photon"# is the energy of the photon#W# is the work function of the metal
So in order to have
#E_"photon" > W#
The kinetic energy of the electron will reach its maximum value when the electron absorbs all the energy of the photon that does not go into overcoming the work function.
So use the Rydberg equation and the Planck  Einstein relation to find the energy of the photons emitted during the
You have
#1/(lamda) = R * (1/n_f^2  1/n_i^2)# Here
#R# is the Rydberg constant, equal to#1.097 * 10^(7)# #"m"^(1)# #lamda# is the wavelength of the photon
and
#E = (h * c)/lamda# Here
#E# is the energy of the photon#h# is Planck's constant, equal to#6.626 * 10^(34)color(white)(.)"J s"# #c# is the speed of light in a vacuum, usually given as#3 * 10^8color(white)(.)"m s"^(1)#
You can combine these two equations to get
#(h * c)/E = 1/R * 1/((1/n_f^2  1/n_i^2))#
Rearrange to solve for
#E = (n_i^2  n_f^2)/ (n_i^2 * n_f^2) * h * R * c#
Plug in the values to find
#E = (3^2  1^2)/(3^2 * 1^2) * 6.626 * 10^(34)"J" color(red)(cancel(color(black)("s"))) * 1.097 * 10^7color(red)(cancel(color(black)("m"^(1)))) * 3 * 10^8 color(red)(cancel(color(black)("m"))) color(red)(cancel(color(black)("s"^(1))))#
#E = 1.938 * 10^(18)# #"J"#
To convert this to electronvolts, use the fact that
#"1 eV" = 1.6 * 10^(19)# #"J"#
You will end up with
#1.938 * 10^(18) color(red)(cancel(color(black)("J"))) * "1 eV"/(1.6 * 10^(19)color(red)(cancel(color(black)("J")))) = "12.11 eV"#
Finally, use equation
#"K"_"E" = "12.11 eV"  "6.08 eV"#
#color(darkgreen)(ul(color(black)("K"_"E" = "6.03 eV" ~~ "6 eV")))#
So I would say that your answer is (2)