Question

# Astronomers have detected hydrogen atoms in interstellar space in the n =744 excited state. Suppose an...

Astronomers have detected hydrogen atoms in interstellar space in the n =744 excited state. Suppose an atom in this excited state undergoes a transition from n =744 to n = 731.

What is the atom's change in energy as a 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?

A) change in energy

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 – 1/744 ^2)

E = 1.41192*10^-25 J/photon (released)

b)

find WL :

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 = wavelength in meters

WL = (6.626*10^-34)(3*10^8)/(1.41192*10^-25)

WL = 1.4078 m

c)