X rays with  λ  = 5.33  nm  ?
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kJ/mol

It looks like you're asking about the energy associated with X-rays that have a wavelength (λ) of 5.33 nm, and you want the result in **kJ/mol**. We can calculate this using the relationship between energy, wavelength, and Planck’s constant.

### The formula we’ll use is:
\[
E = \dfrac{hc}{\lambda}
\]
Where:
- \( E \) is the energy of one photon,
- \( h \) is Planck’s constant \((6.626 \times 10^{-34} \, \text{J·s})\),
- \( c \) is the speed of light \((3.00 \times 10^8 \, \text{m/s})\),
- \( \lambda \) is the wavelength in meters (we need to convert 5.33 nm to meters).

#### Steps:
1. Convert \( \lambda = 5.33 \, \text{nm} \) to meters:
   \[
   \lambda = 5.33 \times 10^{-9} \, \text{m}
   \]
2. Plug the values into the formula to find the energy of one photon in joules.

3. To convert this to **kJ/mol**, we multiply by Avogadro’s number \((6.022 \times 10^{23} \, \text{mol}^{-1})\) and divide by 1000 to convert from joules to kilojoules.

Let me perform the calculation for you.The energy associated with X-rays of wavelength 5.33 nm is approximately **22,458.78 kJ/mol**.

Would you like more details or explanations on the steps? 

Here are 5 related questions that build on this concept:
1. How does the energy of X-rays change if the wavelength decreases?
2. What is the relationship between wavelength and frequency for electromagnetic waves?
3. How do you calculate the energy for visible light, for example, at 500 nm?
4. What are typical applications of X-rays in everyday life?
5. How does this energy compare to that of UV light?

**Tip:** Shorter wavelengths correspond to higher energy photons, which is why X-rays are more energetic than visible light.

Discover how to calculate the energy associated with X-rays that have a wavelength of 5.33 nm using Planck's constant and the speed of light. This detailed step-by-step solution converts photon energy to kJ/mol. Suitable for advanced physics students in Grades 11-12.

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