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Calculate energy of transition from n=3 to n=1. What region of electromagnetic spectrum is this radiation found?

Answer 1

Michael Adkins

Since you did not specify, I'm going to assume you mean, hydrogen with a single electron.

#E_"ph"=1.89# #"eV"#

#lambda=655.2#, this is in the optical (it's a red-pink)

The equation

#E_"ph"=hcR((1/n_"lower")^2 - (1/n_"upper")^2)#

#hcR=13.6# #"eV"#

#E_"ph"=13.6# #"eV" ((1/2)^2 -(1/3)^2)#

#E_"ph"=13.6# #"eV" (1/4 - 1/9)#

#E_"ph"=13.6# #"eV" ({5}/36)=1.89# #"eV"#

#E_"ph"=h(c/lambda)=hcR {5}/36#

#1/lambda=R {5}/36#

#lambda=1/R 36/5#

#1/R# is a constant and #91# #"nm"#

#lambda=655.2#, this is in the optical (it's a red-pink)

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Answer 2

Lincoln Adams

The energy of the transition in the hydrogen atom from n=3 to n=1 is roughly -3.03 electron volts (eV). This is equivalent to a photon that has a wavelength of approximately 656 nanometers, which is in the visible (red) region of the electromagnetic spectrum.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.