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
Anvisha [2.4K]
3 years ago
15

A photon of wavelength 7.33 pm scatters at an angle of 157° from an initially stationary, unbound electron. What is the de Brogl

ie wavelength of the electron after the photon has been scattered?
Physics
1 answer:
Ann [662]3 years ago
8 0

Answer:

4.63 p.m.

Explanation:

The problem given here can be solved by the Compton effect which is expressed as

\lambda^{'}-\lambda=\frac{h}{m_e c}(1-cos\theta)

here, \lambda  is the initial photon wavelength, \lambda^{'} is the scattered photon wavelength, h is he Planck's constant, m_e is the free electron mass, c is the velocity of light, \theta  is the angle of scattering.

Given that, the scattering angle is, \theta=157^{\circ}

Putting the respective values, we get

\lambda^{'}-\lambda=\frac{6.626\times 10^{-34} }{9.11\times 10^{-31}\times 3\times 10^{8}  } (1-cos157^\circ ) m\\\lambda^{'}-\lambda=2.42\times 10^{-12} (1-cos157^\circ ) m\\\lambda^{'}-\lambda=2.42(1-cos157^\circ ) p.m.

Therfore,

\lambda^{'}-\lambda=4.64 p.m.

Here, the photon's incident wavelength is \lamda=7.33pm

So,

\lambda^{'}=7.33+4.64=11.97 p.m

From the conservation of momentum,

\vec{P_\lambda}=\vec{P_{\lambda^{'}}}+\vec{P_e}

here, \vec{P_\lambda} is the initial photon momentum, \vec{P_{\lambda^{'}}} is the final photon momentum and \vec{P_e} is the scattered electron momentum.

Expanding the vector sum, we get

P^2_{e}=P^2_{\lambda}+P^2_{\lambda^{'}}-2P_\lambda P_{\lambda^{'}}cos\theta

Now expressing the momentum in terms of De-Broglie wavelength

P=h/\lambda and putting it in the above equation we get,

\lambda_{e}=\frac{\lambda \lambda^{'}}{\sqrt{\lambda^{2}+\lambda^{2}_{'}-2\lambda \lambda^{'} cos\theta}}

Therfore,

\lambda_{e}=\frac{7.33\times 11.97}{\sqrt{7.33^{2}+11.97^{2}-2\times 7.33\times 11.97\times cos157^\circ }} p.m.\\\lambda_{e}=\frac{87.7401}{18.935} = 4.63 p.m.

This is the de Broglie wavelength of the electron after scattering.

You might be interested in
What transfers energy in the form of vibrating electric and magnetic fields?
Rashid [163]
Electromagnetic waves are waves that consist of vibrating electric and magnetic fields. They transfer energy through matter or across space. The transfer of energy by electromagnetic waves is called electromagnetic radiation. ... The two vibrating fields together form an electromagnetic wave.
5 0
3 years ago
Read 2 more answers
If you traveled one mile at a speed of 100 miles per hour and another mile at a speed if 1 mile per hour, your average speed wou
Semenov [28]

Answer:

v = 1.98 mph

Explanation:

Given that,

Speed to travel one mile is 100 mph

Speed to travel another mile is 1 mph

The formula used to find your average speed is given by :

v=\dfrac{2v_1v_2}{v_1+v_2}

Putting the values, we get :

v=\dfrac{2\times 100\times 1}{100+1}

v = 1.98 mph

So, yours average speed is 1.98 mph.

7 0
3 years ago
A 2.0-kilogram cantaloupe rolling north at 4.0 meters per second collides head on with a 1.0-kilogram orange rolling south at 8.
Murrr4er [49]

Answer:

Hi how are you doing today Jasmine

8 0
2 years ago
Read 2 more answers
Calculating heat gained or lost requires mass, specific heat, and
Anarel [89]
<span>Calculating heat gained or lost requires mass, specific heat, and

</span><span>c. change in temperature.</span><span>

</span>
6 0
3 years ago
Females are the only gender capable of suffering from an eating disorder.<br> A. true<br> B. false
AnnZ [28]
ANSWER
That’s false!!
8 0
3 years ago
Other questions:
  • A person standing at the edge of a seaside cliff kicks a stone, horizontally over the edge with a velocity of 18 m/s. The cliff
    7·1 answer
  • Thoroughly explain how to balance this chemical equation.
    15·1 answer
  • An underwater diver sees the sun 50° above horizontal. how high is the sun above the horizon to a fisherman in a boat above the
    11·1 answer
  • A race car travels 765 km around a circular sprint track of radius 1.263 km. How many times did it go around the track?
    5·1 answer
  • Darwin is sitting on top of a 10 m tree and decided to drop a 3 kg baseball to the ground. What is the velocity when the PE turn
    12·1 answer
  • Which color is in the middle of the light spectrum?
    10·1 answer
  • HELP ASAP
    14·1 answer
  • Mainly need help with part A. No links, thanks!​
    6·1 answer
  • A car starts from rest and after 5.5 seconds it is moving at 30 m/s. What is the value of t? Use one of the following to find th
    10·1 answer
  • If two objects have different tempters, in which direction will heat move? for how long
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!