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In: Chemistry

For the hydrogen atom, the transition from the 2p state to the 1s state is accompanied...

For the hydrogen atom, the transition from the 2p state to the 1s state is accompanied by the emission of a photon with an energy of 16.2×10-19 J. For a C atom, the same transition (2p to 1s) is accompanied by the emission of x-rays of wavelength 44.7 Å. What is the energy difference between these states in carbon?

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The energy difference between these states in carbon is _________larger than smaller than about the same as the corresponding energy difference for hydrogen.

The energy difference between these states in oxygen would be expected to be _________larger than smaller than about the same as the corresponding energy difference for carbon.

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Expert Solution

The energy transition will be equal to 1.55⋅10−19J.

So, you know your energy levels to be n = 5 and n = 3. Rydberg's equation will allow you calculate the wavelength of the photon emitted by the electron during this transition

1λ=R⋅(1n2final−1n2initial), where

λ - the wavelength of the emitted photon;
R - Rydberg's constant - 1.0974⋅107m−1;
nfinal - the final energy level - in your case equal to 3;
ninitial - the initial energy level - in your case equal to 5.

So, you've got all you need to solve for λ, so

1λ=1.0974⋅107m−1⋅(132−152)

1λ=0.07804⋅107m−1⇒λ=1.28⋅10−6m

Since E=hcλ, to calculate for the energy of this transition you'll have to multiply Rydberg's equation by h⋅c, where

h - Planck's constant - 6.626⋅10−34J⋅s
c - the speed of light - 299,792,458 m/s

So, the transition energy for your particular transition (which is part of the Paschen Series) is

E=6.626⋅10−34J⋅s⋅299,792,458m/s1.28⋅10−6m

E=1.55⋅10−19J


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