Calculate the wavelength of the X-ray.
Understand the Problem
The question is asking to calculate the wavelength of an X-ray given its frequency and wave speed. It indicates using the formula wave speed = frequency × wavelength, suggesting a straightforward application of this formula to solve for the wavelength.
Answer
The wavelength of the X-ray is $\lambda = 1.5 \times 10^{-8} \, \text{m}$.
Answer for screen readers
The wavelength of the X-ray is $\lambda = 1.5 \times 10^{-8} , \text{m}$.
Steps to Solve
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Identify the formula to use The formula relating wave speed ($v$), frequency ($f$), and wavelength ($\lambda$) is given by: $$ v = f \times \lambda $$
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Rearrange the formula To find the wavelength ($\lambda$), we can rearrange the formula to solve for $\lambda$: $$ \lambda = \frac{v}{f} $$
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Substitute the values Substituting the given values of wave speed and frequency into the formula:
- Wave speed, $v = 300,000,000 , \text{m/s}$
- Frequency, $f = 2.0 \times 10^{16} , \text{Hz}$ So, we have: $$ \lambda = \frac{300,000,000 , \text{m/s}}{2.0 \times 10^{16} , \text{Hz}} $$
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Calculate the wavelength Now perform the division to find the wavelength: $$ \lambda = \frac{300,000,000}{2.0 \times 10^{16}} $$
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Simplify the calculation Calculating this gives: $$ \lambda = 1.5 \times 10^{-8} , \text{m} $$
The wavelength of the X-ray is $\lambda = 1.5 \times 10^{-8} , \text{m}$.
More Information
Wavelengths of X-rays typically range from about $0.01 , \text{nm}$ to $10 , \text{nm}$, indicating that the wavelength we've calculated is within the X-ray spectrum.
Tips
- Forgetting to convert units: Ensure all units are consistent, particularly when dealing with the speed of light and frequencies in different units.
- Misusing the equation: Be careful not to mix up the formula, as the relationship is specific and directly affects the answer.
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