Question

# Astronomers have detected hydrogen atoms in interstellar space in the n=746 excited state. Suppose an atom...

Astronomers have detected hydrogen atoms in interstellar space in the n=746 excited state. Suppose an atom in this excited state undergoes a transition from n=746 to n=731. What is the atoms change in energy as the result of this transition? What is the wavelength of radiation corresponding to this transition? What kind of telescope would astronomers need in order to detect radiation of this wavelength?

Apply Rydberg Formula

E = R*(1/nf^2 – 1/ni ^2)

R = -2.178*10^-18 J

Nf = final stage/level

Ni = initial stage/level

E = Energy per unit (i.e. J/photon)

E = (-2.178*10^-18)*(1/731^2 – 1/746 ^2)

E = 1.6226*10^-25 J/atom

For the wavelength:

WL = h c / E

h = Planck Constant = 6.626*10^-34 J s

c = speed of particle (i.e. light) = 3*10^8 m/s

E = energy per particle J/photon

WL = (6.626*10^-34)(3*10^8)/(1.6226*10^-25)

WL = 1.2250 m

c)

A radio telescope will do, it will be able to review "meters" or 10^0 meter of wavleenght