Question

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?

Answer #1

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

This is RADIO waves adiation

c)

we need RADIO telescopes

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Please show
your full work!! Where you got number from step by step

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