To find the wavelength of the L absorption edge in Uranium (Z=92), we can follow these steps:
### Step 1: Calculate the energy corresponding to the K absorption edge.
The energy of the K absorption edge can be calculated using the formula:
\[
E_K = \frac{hc}{\lambda_K}
\]
where:
- \(h\) is Planck's constant (approximately \(4.14 \times 10^{-15} \, \text{eV s}\)),
- \(c\) is the speed of light (approximately \(3 \times 10^8 \, \text{m/s}\)),
- \(\lambda_K\) is the wavelength of the K absorption edge (given as \(0.107 \, \text{Å}\)).
First, we convert the wavelength from Ångströms to meters:
\[
0.107 \, \text{Å} = 0.107 \times 10^{-10} \, \text{m}
\]
Now, substituting the values:
\[
E_K = \frac{(4.14 \times 10^{-15} \, \text{eV s})(3 \times 10^8 \, \text{m/s})}{0.107 \times 10^{-10} \, \text{m}} \approx 115.9 \, \text{keV}
\]
### Step 2: Calculate the energy corresponding to the Kα line.
Using the same formula for the Kα line:
\[
E_{K\alpha} = \frac{hc}{\lambda_{K\alpha}}
\]
where \(\lambda_{K\alpha} = 0.126 \, \text{Å}\).
Converting the wavelength:
\[
0.126 \, \text{Å} = 0.126 \times 10^{-10} \, \text{m}
\]
Now substituting the values:
\[
E_{K\alpha} = \frac{(4.14 \times 10^{-15} \, \text{eV s})(3 \times 10^8 \, \text{m/s})}{0.126 \times 10^{-10} \, \text{m}} \approx 98.4 \, \text{keV}
\]
### Step 3: Calculate the energy corresponding to the L absorption edge.
Using the relationship:
\[
E_{K\alpha} = E_K - E_L
\]
we can rearrange this to find \(E_L\):
\[
E_L = E_K - E_{K\alpha}
\]
Substituting the values we calculated:
\[
E_L = 115.9 \, \text{keV} - 98.4 \, \text{keV} = 17.5 \, \text{keV}
\]
### Step 4: Calculate the wavelength of the L absorption edge.
Using the energy of the L absorption edge, we can find the wavelength:
\[
\lambda_L = \frac{hc}{E_L}
\]
Substituting the values:
\[
\lambda_L = \frac{(4.14 \times 10^{-15} \, \text{eV s})(3 \times 10^8 \, \text{m/s})}{17.5 \times 10^3 \, \text{eV}} \approx 0.709 \, \text{Å}
\]
### Final Answer:
The wavelength of the L absorption edge is approximately \(0.709 \, \text{Å}\), which can be rounded to \(0.7 \, \text{Å}\).
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