# According to the Bohr model for the hydrogen atom, how much energy is necessary to excite an electron from n=1 to n=2?

##### 1 Answer

This energy can be determined from the **Rydberg equation**, which is

#\mathbf(1/lambda = R_H(1/(n_i^2) - 1/(n_j^2)))# where:

#lambda# is thewavelengthin units of#"m"# .#R_H# is theRydberg constant,#"10973731.6 m"^-1# .#n_i# is theprincipal quantum number#n# for thelowerenergy level.#n_j# is theprincipal quantum number#n# for thehigherenergy level.

In this case, **upwards**. Thus:

#1/lambda = "10973731.6 m"^-1(1/1^2 - 1/2^2)#

#= "10973731.6 m"^-1(1/1^2 - 1/2^2)#

#= "8230298.7 m"^(-1)#

Now, the wavelength is

#color(green)(lambda) = 1/("8230298.7 m"^(-1))#

#= color(green)(1.215xx10^(-7) "m"),#

or

#\mathbf(DeltaE = hnu = (hc)/lambda)# where:

#DeltaE# is thechangeinenergyin#"J"# .#h# isPlanck's constant,#6.626xx10^(-34) "J"cdot"s"# .#nu# is thefrequencyin#"s"^(-1)# . Remember that#c = lambdanu# .#c# is thespeed of light,#2.998xx10^8 "m/s"# .#lambda# is thewavelengthin#"m"# like before.

So, the **absorption of energy** into a *single* hydrogen atomic system associated with this process is:

#color(blue)(DeltaE) = ((6.626xx10^(-34) "J"cdotcancel"s")(2.998xx10^(8) cancel"m/s"))/(1.215xx10^(-7) cancel"m")#

#= color(blue)(1.635xx10^(-18) "J")#

(absorption is an increase in energy for the system, thus