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Chapter 7: Problem 19

When copper is bombarded with high-energy electrons, X rays are emitted. Calculate the energy (in joules) associated with the photons if the wavelength of the X rays is \(0.154 \mathrm{nm}\).

Short Answer

Expert verified
The energy associated with the photons is approximately \(1.29 \times 10^{-15}\) Joules.

Step by step solution

01

Write down the known values

We know the wavelength (\(\lambda\)) is \(0.154 \mathrm{nm}\), which needs to be converted to meters for consistency in SI units. Additionally, Planck's constant (h) is \(6.63 \times 10^{-34} \mathrm{J \cdot s}\), and the speed of light (c) is \(3.0 \times 10^8 \mathrm{m/s}\).
02

Convert the wavelength to meters

\(\lambda = 0.154 \times 10^{-9}\) m, as 1nm equals to \(10^{-9}\) meters.
03

Substitute values into the formula

We plug these values into the equation \(E = \frac{hc}{\lambda}\) to get \(E = \frac{6.63 \times 10^{-34} \mathrm{J \cdot s} \times 3.0 \times 10^8 \mathrm{m/s}}{0.154 \times 10^{-9} m}\).
04

Do the calculation

By performing the calculations, we find that the energy \(E\) of the X-ray photons is approximately \(1.29 \times 10^{-15}\) Joules.

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