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Chapter 29: Q53PE (page 1064)

Find the wavelength of a proton moving at 1.00 % of the speed of light.

Short Answer

Expert verified

The wavelength of a proton is obtained as \[1.32 \times {10^{ - 13}}\;{\rm{ma}}\].

Step by step solution

01

Define formula for the wavelength.

Consider the formula for the proton is:

\[\lambda = \frac{h}{{mv}}\]

Here, h is the plank鈥檚 constant, v is the velocity of the photon and m is the mass of the proton.

02

Evaluate the wavelength

Substitute the values and solve for the wavelength as:

\[\begin{array}{c}\lambda = \frac{{6.63 \times {{10}^{ - 34}}\;{\rm{J}} \cdot {\rm{s}}}}{{1.67 \times {{10}^{ - 27}}\;{\rm{kg}} \times 0.01 \times 3.00 \times {{10}^8}\;\frac{{\rm{m}}}{{\rm{s}}}}}\\ = 1.32 \times {10^{ - 13}}\;{\rm{m}}\end{array}\]

Therefore, the wavelength is\[{\rm{1}}{\rm{.32}} \times {\rm{1}}{{\rm{0}}^{ - {\rm{13}}}}{\rm{ m}}\].

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Most popular questions from this chapter

What is the maximum kinetic energy in eV of electrons ejected from sodium metal by \(450\,{\rm{nm EM}}\) radiation, given that the binding energy is \(2.28\,{\rm{eV}}\)?

The difference in energy between allowed oscillator states in HBr molecules is 0.0330eV. What is the oscillation frequency of this molecule?

Take the ratio of relativistic rest energy, \[{\bf{E = \gamma m}}{{\bf{c}}^{\bf{2}}}\], to relativistic momentum, \[{\bf{p = \gamma mu}}\], and show that in the limit that mass approaches zero, you find\[\frac{{\bf{E}}}{{\bf{p}}}{\bf{ = c}}\].

Integrated Concepts

(a) What is the separation between double slits that produces a second order minimum at 45.0o for 650 - nm light?

(b) What slit separation is needed to produce the same pattern for 1.00 keV protons.

What is the accelerating voltage of an x-ray tube that produces x rays with a shortest wavelength of \({\rm{0}}{\rm{.0103 nm}}\)?
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