Question

# (a) Calculate the ratio of $\mathrm{K}_{\alpha}$ wavelengths for uranium and carbon. (b) Calculate the ratio of $\mathrm{L}_{\alpha}$ wavelengths for platinum and calcium.

Solution

Verified
Step 1
1 of 3

Expression for $K_{\alpha}$ is

\begin{align*} \lambda_{K_{\alpha}} &= \frac{4}{3 R} \frac{1} { \left( Z - 1 \right)^2} \tag{1}. \end{align*}

We are asked to calculate ratio of $K_{\alpha}$ wavelengths for uranium and carbon, which have atomic number of 92 and 6. So, using eqaution (1), we get

\begin{align*} \frac{ \lambda_{K_{\alpha}, U}}{ \lambda_{K_{\alpha}, C}} &= \frac{\frac{1} { \left( 92 - 1 \right)^2}}{\frac{1} { \left( 6 - 1 \right)^2}} \\ \frac{ \lambda_{K_{\alpha}, U}}{ \lambda_{K_{\alpha}, C}} &= \frac{5^2}{91^2} \\ \frac{ \lambda_{K_{\alpha}, U}}{ \lambda_{K_{\alpha}, C}} &= \boxed{3.02 \cdot 10^{-3} } \end{align*}

## Recommended textbook solutions

#### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th EditionISBN: 9780133942651 (5 more)Randall D. Knight
3,508 solutions

#### Modern Physics for Scientists and Engineers

4th EditionISBN: 9781133103721 (3 more)Andrew Rex, Stephen T. Thornton
1,122 solutions

#### Physics for Scientists and Engineers

9th EditionISBN: 9781133947271 (2 more)John W. Jewett, Raymond A. Serway
6,057 solutions

#### Classical Mechanics

1st EditionISBN: 9781891389221 (5 more)John R. Taylor
741 solutions