How do you determine which of these hydrogen atom energy transitions has the highest energy difference? Isn't it #(4)# since it is the odd one out?
#1)# #n = 4->2#
#2)# #n = 5->2#
#3)# #n = 7->2#
#4)# #n = 2->1#
1 Answer
It is actually
Well, you can compare options (1), (2), and (4) and see that since
Looking at
#DeltaE = -hcR_H(1/n_f^2 - 1/n_i^2)#
#DeltaE_(4->2) = -(6.626 xx 10^(-34) "J"cdot"s")(2.998 xx 10^(8) "m/s")("109737 m"^(-1))(1/2^2 - 1/4^2)#
#= 4.087 xx 10^(-21) "J"#
#DeltaE_(2->1) = -(6.626 xx 10^(-34) "J"cdot"s")(2.998 xx 10^(8) "m/s")("109737 m"^(-1))(1/1^2 - 1/2^2)#
#= 1.635 xx 10^(-20) "J"#
In fact, it is NOT. So actually,
#DeltaE_(5->2) = -(6.626 xx 10^(-34) "J"cdot"s")(2.998 xx 10^(8) "m/s")("109737 m"^(-1))(1/2^2 - 1/5^2)#
#= 4.578 xx 10^(-21) "J"#
#DeltaE_(7->2) = -(6.626 xx 10^(-34) "J"cdot"s")(2.998 xx 10^(8) "m/s")("109737 m"^(-1))(1/2^2 - 1/7^2)#
#= 5.005 xx 10^(-21) "J"#
Thus, the energy difference ordering is:
#bb(DeltaE_(2->1) > DeltaE_(7->2) > DeltaE_(5->2) > DeltaE_(4->2))#
or:
#(3) > (4) > (2) > (1)#
Thus, the answer is option (3). Always check your numbers.