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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
Substituting the given values, we get the energy associated with the photons in Joules.

Step by step solution

01

Find the frequency

To find the frequency, rearrange the speed of light equation to \(v = c/\lambda\). Given that \(c = 3.00 x 10^8 ms^{-1}\) and \(\lambda = 0.154 nm = 0.154 x 10^{-9} m\), calculate \(v = c/\lambda\).
02

Calculate the energy'

Substitute the Planck's constant \(h\) and frequency \(v\) into the energy equation \(E = hv\). Given that \(h = 6.63 x 10^{-34} Js\), and use the frequency \(v\) from Step 1, we calculate the energy \(E\).
03

Converting the units correctly

Make sure that the units are consistent throughout. For instance, be very careful with the conversion of nanometers to meters in step 1.

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Most popular questions from this chapter

Why do the \(3 s, 3 p,\) and \(3 d\) orbitals have the same energy in a hydrogen atom but different energies in a many-electron atom?

Determine the maximum number of electrons that can be found in each of the following subshells: \(3 s\), \(3 d, 4 p, 4 f, 5 f\)

Explain why elements produce their own characteristic colors when they emit photons.

Protons can be accelerated to speeds near that of light in particle accelerators. Estimate the wavelength (in \(\mathrm{nm}\) ) of such a proton moving at \(2.90 \times\) \(10^{8} \mathrm{~m} / \mathrm{s}\). (Mass of a proton \(\left.=1.673 \times 10^{-27} \mathrm{~kg} .\right)\)

Discuss the similarities and differences between a \(1 s\) and a \(2 s\) orbital.
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