Benzene, C6H6, has a cyclic structure where the carbon atoms make a hexagon. The π electrons in the cyclic molecule can be approximated as having two-dimensional rotational motion. Calculate the diameter of this “electron ring” if it is assumed that a transition occurring at 260.0 nm corresponds to an electron going from m = 3 to m = 4.
To calculate the diameter of the "electron ring" in benzene, we can use the formula for the diameter of a circular path:
d = λ / (2π)
where: d is the diameter of the circular path, λ is the wavelength of the transition, and π is a mathematical constant approximately equal to 3.14159.
In this case, the transition wavelength (λ) is given as 260.0 nm.
Substituting the values into the formula, we get:
d = 260.0 nm / (2π)
To convert the wavelength from nanometers (nm) to meters (m), we divide by 10^9:
d = (260.0 × 10^(-9) m) / (2π)
Now we can calculate the diameter:
d ≈ 4.142 × 10^(-8) m / π
Using the approximation of π as 3.14159, we can evaluate the expression:
d ≈ 1.317 × 10^(-8) m
Therefore, the diameter of the "electron ring" in benzene, based on the given transition wavelength, is approximately 1.317 × 10^(-8) meters.
Benzene, C6H6, has a cyclic structure where the carbon atoms make a hexagon.
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