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Chapter 29: Q19CQ (page 1061)

Which formula may be used for the momentum of all particles, with or without mass?

Short Answer

Expert verified

De-Broglie鈥檚 formula could be used for mass and mass-less particles:

\[{\rm{p = }}\frac{{\rm{h}}}{{\rm{\lambda }}}\]

Step by step solution

01

Formula to describe the momentum of particles

As per De-Broglie's hypothesis which is all microscopic particles, whether mass-less, like photons or having mass, like electrons, have wave properties. Where the relationship between momentum and wavelength is fundamental for all particles. So, we can use this formula to describe the momentum of all particles with or without mass:

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

02

De- Broglie’s formula

Where, \[{\rm{p}}\]is the momentum, \[{\rm{h}}\] is Planck's constant and \[{\rm{\lambda }}\] is the wavelength.

Therefore, De-Broglie鈥檚 formula could be used for mass and mass-less particles:

\[{\rm{p = }}\frac{{\rm{h}}}{{\rm{\lambda }}}\]

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Most popular questions from this chapter

(a) Calculate the number of photoelectrons per second ejected from a \(1.00\,{\rm{m}}{{\rm{m}}^{\rm{2}}}\) area of sodium metal by \(500\,{\rm{nm EM}}\) radiation having an intensity of \(1.30\,{\rm{kW/}}{{\rm{m}}^{\rm{2}}}\) (the intensity of sunlight above the Earth鈥檚 atmosphere). (b) Given that the binding energy is\(2.28\,{\rm{eV}}\), what power is carried away by the electrons? (c) The electrons carry away less power than brought in by the photons. Where does the other power go? How can it be recovered?

How many x-ray photons per second are created by an x-ray tube that produces a flux of x rays having a power of \({\rm{1}}{\rm{.00 - W}}\)? Assume the average energy per photon is \({\rm{75}}{\rm{.0 - keV}}\).

(a) If the position of an electron in a membrane is measured to an accuracy of 1.00 渭m , what is the electron鈥檚 minimum uncertainty in velocity?

(b) If the electron has this velocity, what is its kinetic energy in eV?

(c) What are the implications of this energy, comparing it to typical molecular binding energies?

Suppose the velocity of an electron in an atom is known to an accuracy of 2.0 x 103 (reasonably accurate compared with orbital velocities). What is the electron鈥檚 minimum uncertainty in position, and how does this compare with the approximate 0.1 nm size of the atom?

Question: Violet light of wavelength \[{\rm{400 nm}}\] ejects electrons with a maximum kinetic energy of \[{\rm{0}}{\rm{.860 eV}}\] from sodium metal. What is the binding energy of electrons to sodium metal?
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