Question

In: Physics

The absorption spectrum of an atom consists of the wavelengths 200 nm, 300nm, and 500 nm....

The absorption spectrum of an atom consists of the wavelengths 200 nm, 300nm, and 500 nm.

a) Draw the atom's energy-level diagram.

b) What wavelengths are seen in the atom's emission spectrum?

(Please show all the steps and calculations with simple explanation. Thank you)

Expert Solution

Absorption Spectrum implies the wavelength of photon required by electron to jump from one energy level to another energy level.

Since energy required to jump from level 1 to level 4 is maximum so it corresponds to 200nm

Similarly 300 nm corresponds to transition from level 1 to level 3

and 500 nm corresponds to transition from level 1 to level 2

Same photon will be released if the transition is same.

So

lambda41 = 200nm

lambda31= 300nm

lambda21 = 500nm

If the electron jumps from level 4 to level 2, the energy between these two levels is the difference of the energy of the photon required to reach these levels. Since energy is inversly proportional to lambda(E = hc/(lambda) )

we get

hc/(lambda42) = hc/lambda41 - hc/lambda21

1/lambda42 = 1/lambda41 - 1/lambda21

We get

lambda42 = (1/(1/200 - 1/500)) = 333.33 nm

Similarly

lambda 43 = (1/(1/200 - 1/300))= 600 nm

lambda 32 = (1/(1/300 - 1/500)) = 750nm

genius_generous answered 1 hour ago

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