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- Introduction to quantum physics
- The wave nature of matter
Using the definition of the de Broglie wavelength, explain how wavelike properties of matter increase with a decrease in mass or decrease in speed. Use as examples an electron (mass = 9.11 × 10
–31 kg) with a speed of 5.0 × 10
6 m/s and a proton (mass = 1.67 × 10
–27 kg) with a speed of 8.0 × 10
6 m/s.
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Test prep for ap courses
In a Davisson-Germer type of experiment, a crystal with a parallel-plane separation (
d ) of 9.1 × 10
–2 nm produces constructive interference with an electron beam at an angle of
θ = 50°. Which of the following is the maximum de Broglie wavelength for these electrons?
- 0.07nm
- 0.09 nm
- 0.14 nm
- 0.21 nm
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In a Davisson-Germer experiment, electrons with a speed of 6.5 × 10
6 m/s exhibit third-order (
n = 3) constructive interference for a crystal with unknown plane separation,
d . Given an angle of incidence of
θ = 45°, compute the value for
d . Compare the de Broglie wavelength to electromagnetic radiation with the same wavelength. (Recall that the mass of the electron is 9.11 × 10
–31 kg.)
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Section summary
- Particles of matter also have a wavelength, called the de Broglie wavelength, given by
, where
is momentum.
- Matter is found to have the same
interference characteristics as any other wave.
Conceptual questions
Problems&Exercises
At what velocity does a proton have a 6.00-fm wavelength (about the size of a nucleus)? Assume the proton is nonrelativistic. (1 femtometer =
)
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Experiments are performed with ultracold neutrons having velocities as small as 1.00 m/s. (a) What is the wavelength of such a neutron? (b) What is its kinetic energy in eV?
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(a) Find the velocity of a neutron that has a 6.00-fm wavelength (about the size of a nucleus). Assume the neutron is nonrelativistic. (b) What is the neutron’s kinetic energy in MeV?
(a)
(b)
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(a) Calculate the velocity of an electron that has a wavelength of
(b) Through what voltage must the electron be accelerated to have this velocity?
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The velocity of a proton emerging from a Van de Graaff accelerator is 25.0% of the speed of light. (a) What is the proton’s wavelength? (b) What is its kinetic energy, assuming it is nonrelativistic? (c) What was the equivalent voltage through which it was accelerated?
(a) 5.29 fm
(b)
(c) 29.4 MV
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Unreasonable Results
(a) Assuming it is nonrelativistic, calculate the velocity of an electron with a 0.100-fm wavelength (small enough to detect details of a nucleus). (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
(a)
(b) This is thousands of times the speed of light (an impossibility).
(c) The assumption that the electron is non-relativistic is unreasonable at this wavelength.
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Questions & Answers
differentiate between demand and supply
giving examples
differentiated between demand and supply using examples
Lambiv
how is the graph works?I don't fully understand
hi guys good evening to all
Lambiv
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
Can I ask you other question?
Shukri
What is different between quantity demand and demand?
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
how do you save a country economic situation when it's falling apart
what is the difference between economic growth and development
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
any question about economics?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
What is the difference between perfect competition and monopolistic competition?
Mohammed
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Source:
OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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