What is the energy absorbed when the electron in a hydrogen atom jumps from #n = 3# to #n=8#?

1 Answer
Sep 19, 2016

The energy is #2.080 × 10^"-19"color(white)(l) "J"#.

Explanation:

We use the Rydberg formula to calculate the transition energies of a hydrogen atom.

#color(blue)(bar(ul(|color(white)(a/a) ΔE = R_E(1/n_i^2 - 1/n_f^2)color(white)(a/a)|)))" "#

where

#ΔE# = energy absorbed or released
#R_E# = Rydberg constant in energy units
#n_i# = initial energy level
#n_f# = final energy level

In your problem,

#R_E = 2.178 × 10^"-18"color(white)(l) "J"#
#n_i = 3#
#n_f = 8#

#ΔE = 2.178 × 10^"-18"color(white)(l) "J"(1/3^2 - 1/8^2) = 2.178 × 10^"-18"color(white)(l) "J"(1/9 - 1/64)#

#= 2.178 × 10^"-18" color(white)(l)"J"((64-9)/(64 × 9)) = 2.178 × 10^"-18"color(white)(l) "J" × 55/(64 × 9)#

#= +2.080 × 10^"-19"color(white)(l) "J"#

The positive sign tells you that the atom has absorbed energy.