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Chapter 27: Problem 69

What potential difference must be applied to an x-ray tube to produce x-rays with a minimum wavelength of \(45.0 \mathrm{pm} ?\)

Short Answer

Expert verified
Answer: The required potential difference is approximately 2.94 x 10^4 V.

Step by step solution

01

Convert the given wavelength from pm to meters

First, we need to convert the given minimum wavelength from picometers to meters: \(\lambda_\text{min} = 45.0 \mathrm{pm} \times \dfrac{1 \mathrm{m}}{10^{12} \mathrm{pm}} = 45.0 \times 10^{-12} \mathrm{m}\)
02

Rearrange the Duane-Hunt law to solve for V

Next, we rearrange the Duane-Hunt law to isolate \(V\) on one side of the equation: \(V = \dfrac{hc}{e\lambda_\text{min}}\)
03

Substitute the known values and calculate V

Now, we substitute the known values of \(h\), \(c\), \(e\), and \(\lambda_\text{min}\) into the equation and calculate \(V\): \(V = \dfrac{(6.6261 \times 10^{-34} \mathrm{J\cdot s})(2.9979 \times 10^8 \mathrm{m/s})}{(1.6022 \times 10^{-19} \mathrm{C})(45.0 \times 10^{-12} \mathrm{m})}\) \(V \approx 2.94 \times 10^4 \mathrm{V}\) The required potential difference to produce x-rays with a minimum wavelength of \(45.0 \mathrm{pm}\) is approximately \(2.94 \times 10^4 \mathrm{V}\).

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Most popular questions from this chapter

The photoelectric effect is studied using a tungsten target. The work function of tungsten is 4.5 eV. The incident photons have energy \(4.8 \mathrm{eV} .\) (a) What is the threshold frequency? (b) What is the stopping potential? (c) Explain why, in classical physics, no threshold frequency is expected.
In a photoelectric experiment using sodium, when incident light of wavelength \(570 \mathrm{nm}\) and intensity \(1.0 \mathrm{W} / \mathrm{m}^{2}\) is used, the measured stopping potential is \(0.28 \mathrm{V} .\) (a) What would the stopping potential be for incident light of wavelength \(400.0 \mathrm{nm}\) and intensity \(1.0 \mathrm{W} / \mathrm{m}^{2} ?\) (b) What would the stopping potential be for incident light of wavelength 570 nm and intensity $2.0 \mathrm{W} / \mathrm{m}^{2} ?(\mathrm{c})$ What is the work function of sodium?
A hydrogen atom has an electron in the \(n=5\) level. (a) If the electron returns to the ground state by emitting radiation, what is the minimum number of photons that can be emitted? (b) What is the maximum number that might be emitted?
What is the maximum wavelength of a photon that can create an electron- positron pair?
What is the smallest energy photon that can be absorbed by a hydrogen atom in its ground state?
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