Calculate the momentum of particles which has possible wavelwavelength of 2.5×10"-10 m
Answers
Answered by
2
A molecule of hydrogen gas has a mass of 3.35�10?27kg and a diameter of 1.48�10?10m. What is the kinetic energy at which this molecule's de Broglie wavelength will be equal to its diameter?
Problem-Solving Strategy 39.1: Particles and Waves
IDENTIFY the relevant concepts :
Both particles and light have wavelike properties as well as particlelike properties. The wavelength of a particle is inversely proportional to the momentum, and the frequency is proportional to the energy.
SET UP the problem:
Determine the target variable and decide which equations you will use to calculate it.
EXECUTE the solution as follows:
Use the equation ?=h/p=h/(mv) to relate the momentum p to the wavelength ?, and use the equation E=hf to relate the energy E to the frequency f.
Nonrelativistic kinetic energy may be expressed as either K=(1/2)mv2 or (because p=mv) K=p2/2m. The latter form is often useful in calculations involving the de Broglie wavelength.
Be careful to use consistent units. Lengths, such as wavelengths, are always in meters if you use the other quantities consistently in SI units. If you want a length in nanometers or some other units, don�t forget to convert. Energies may be expressed in either joules or electron volts. Depending on your choice, you can use either h=6.626�10?34J?s or h=4.136�10?15eV?s.
EVALUATE your answer:
To check your numerical results, it helps to remember some typical orders of magnitude for quantities on the atomic scale:
Size of an atom: 10?10m
Mass of an atom: 10?26kg
Mass of an electron: 10?30kg
Energy magnitude of an atomic state: 1 to 10 eV (10?19J to 10?18J) (but some interaction energies are much smaller)
Speed of an electron in the Bohr model of a hydrogen atom: 106m/s
Electron charge magnitude: 10?19C
kT at room temperature: 1/40eV
What is the kinetic energy K0 at which this molecule's de Broglie wavelength will be equal to its diameter?
Express your answer in electron volts to three significant figures.
______________________________________
Problem-Solving Strategy 39.1: Particles and Waves
IDENTIFY the relevant concepts :
Both particles and light have wavelike properties as well as particlelike properties. The wavelength of a particle is inversely proportional to the momentum, and the frequency is proportional to the energy.
SET UP the problem:
Determine the target variable and decide which equations you will use to calculate it.
EXECUTE the solution as follows:
Use the equation ?=h/p=h/(mv) to relate the momentum p to the wavelength ?, and use the equation E=hf to relate the energy E to the frequency f.
Nonrelativistic kinetic energy may be expressed as either K=(1/2)mv2 or (because p=mv) K=p2/2m. The latter form is often useful in calculations involving the de Broglie wavelength.
Be careful to use consistent units. Lengths, such as wavelengths, are always in meters if you use the other quantities consistently in SI units. If you want a length in nanometers or some other units, don�t forget to convert. Energies may be expressed in either joules or electron volts. Depending on your choice, you can use either h=6.626�10?34J?s or h=4.136�10?15eV?s.
EVALUATE your answer:
To check your numerical results, it helps to remember some typical orders of magnitude for quantities on the atomic scale:
Size of an atom: 10?10m
Mass of an atom: 10?26kg
Mass of an electron: 10?30kg
Energy magnitude of an atomic state: 1 to 10 eV (10?19J to 10?18J) (but some interaction energies are much smaller)
Speed of an electron in the Bohr model of a hydrogen atom: 106m/s
Electron charge magnitude: 10?19C
kT at room temperature: 1/40eV
What is the kinetic energy K0 at which this molecule's de Broglie wavelength will be equal to its diameter?
Express your answer in electron volts to three significant figures.
______________________________________
Similar questions