1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
brilliants [131]
3 years ago
7

An electron and a proton each have a thermal kinetic energy of 3kBT/2. Calculate the de Broglie wavelength of each particle at a

temperature of 1800 K. (kb is Boltzmann's constant, 1.38x10^-23 J/K). (1) Wavelength of the electron = ____ m (2) Wavelength of the proton = ______ m
Physics
1 answer:
S_A_V [24]3 years ago
7 0

Answer:

Given:

Thermal Kinetic Energy of an electron, KE_{t} = \frac{3}{2}k_{b}T

k_{b} = 1.38\times 10^{- 23} J/k = Boltzmann's constant

Temperature, T = 1800 K

Solution:

Now, to calculate the de-Broglie wavelength of the electron, \lambda_{e}:

\lambda_{e} = \frac{h}{p_{e}}

\lambda_{e} = \frac{h}{m_{e}{v_{e}}              (1)

where

h = Planck's constant = 6.626\times 10^{- 34}m^{2}kg/s

p_{e} = momentum of an electron

v_{e} = velocity of an electron

m_{e} = 9.1\times 10_{- 31} kg = mass of electon

Now,

Kinetic energy of an electron = thermal kinetic energy

\frac{1}{2}m_{e}v_{e}^{2} = \frac{3}{2}k_{b}T

}v_{e} = \sqrt{2\frac{\frac{3}{2}k_{b}T}{m_{e}}}

}v_{e} = \sqrt{\frac{3\times 1.38\times 10^{- 23}\times 1800}{9.1\times 10_{- 31}}}

v_{e} = 2.86\times 10^{5} m/s                    (2)

Using eqn (2) in (1):

\lambda_{e} = \frac{6.626\times 10^{- 34}}{9.1\times 10_{- 31}\times 2.86\times 10^{5}} = 2.55 nm

Now, to calculate the de-Broglie wavelength of proton, \lambda_{e}:

\lambda_{p} = \frac{h}{p_{p}}

\lambda_{p} = \frac{h}{m_{p}{v_{p}}                             (3)

where

m_{p} = 1.6726\times 10_{- 27} kg = mass of proton

v_{p} = velocity of an proton

Now,

Kinetic energy of a proton = thermal kinetic energy

\frac{1}{2}m_{p}v_{p}^{2} = \frac{3}{2}k_{b}T

}v_{p} = \sqrt{2\frac{\frac{3}{2}k_{b}T}{m_{p}}}

}v_{p} = \sqrt{\frac{3\times 1.38\times 10^{- 23}\times 1800}{1.6726\times 10_{- 27}}}

v_{p} = 6.674\times 10^{3} m/s                               (4)                    

Using eqn (4) in (3):

\lambda_{p} = \frac{6.626\times 10^{- 34}}{1.6726\times 10_{- 27}\times 6.674\times 10^{3}} = 5.94\times 10^{- 11} m = 0.0594 nm

You might be interested in
Help plzzzzzzzzzzzzzzzz!
aksik [14]
 

concave <span>ray diagrams were constructed in order to determine the general location, size, orientation, and type of image formed by concave mirrors. Perhaps you noticed that there is a definite relationship between the image characteristics and the location where an object placed in front of a concave mirror. but, convex</span><span>ray diagrams were constructed in order to determine the location, size, orientation, and type of image formed by concave mirrors. The ray diagram constructed earlier for a convex mirror revealed that the image of the object was virtual, upright, reduced in size and located behind the mirror. </span>
3 0
2 years ago
A person's center of mass is easily found by having the person lie on a reaction board. A horizontal, 2.1-m-long, 6.6 kg reactio
MrRissso [65]
Answer is x hopefully this helps your stupid head
5 0
3 years ago
4. If the Kitty Hawk Flyer has 12 HP, do some research to find out how to express this power in the SI system and report the num
lesya [120]

Product of my research: 1 HP = 746 watts .

12 HP = (12 x 746 W) = 8,952 W

8,952 W = 8.952 kW
8 0
3 years ago
Read 2 more answers
A pulse traveled the length of a stretched spring the pulse transferred...A)energy only B)mass only C)both energy and mass D) ne
xz_007 [3.2K]

Answer:

A

Explanation:

So a pulse is a part of a mechanical wave, and mechanical waves are energy transfer trough some medium, in this case a stretched spring. So the correct answer is (A) energy only. The pulse cant be transferred into mass.

8 0
3 years ago
The greatest ocean depths on the Earth are found in the Marianas Trench near the Philippines. Calculate the pressure (in atm) du
frozen [14]

Answer:

P = 103867260 atm

Explanation:

The pressure at the bottom of any liquid column is equal to product of density of the liquid , gravitational acceleration constant (g) and height of the water column

Thus, P = \rho*g*h

Substituting the given values, we get -

P = 1029 kg/m3 * 9.8 m/s^2  *10.3 *1000 meters

P = 103867260 atm

8 0
2 years ago
Other questions:
  • Two identical objects are moving directly toward one another at the same speed v. ~v â~v m m what is the total kinetic energy of
    15·1 answer
  • A piece of nickel at 25 °C is dropped into a glass of water at 25 °C. Which statement is correct?
    10·1 answer
  • Slow-twitch muscles are needed for what?
    5·2 answers
  • What is mercury barometer​
    13·1 answer
  • As shown in the diagram, two forces act on an object. The forces have magnitudes F1 = 5.7 N and F2 = 1.9 N. What third force wil
    11·1 answer
  • Reaction rate depends on how many molecules come into contact with each other with enough energy to react. How would you increas
    6·1 answer
  • Two very large parallel sheets a distance d apart have their centers directly opposite each other. The sheets carry equal but op
    9·2 answers
  • Light waves have constructive interference because they are emitted _____.
    11·1 answer
  • You want to create an electric field vector E = &lt; 0, 5 104, 0&gt; N/C at location &lt; 0, 0, 0&gt;. Where would you place a p
    14·1 answer
  • You are traveling at 55 mi/h along the x-axis relative to a straight, level road and pass a car that is traveling at 45 mi/h. Th
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!