# 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?

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#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.**