an electron is trapped in an infinite potential well. find its first five energy levels. the width of the potential well is: case 1. 0.10 nanometer case 2. 0.20 nanometer
Answers
The first five energy levels of an electron trapped in an infinite potential well with a width of 0.20 nm are \(4.11 * 10^-^1^9 J\), \(1.64 *10^-^1^8 J\), \(3.70 * 10^-^1^8 J\), \(6.58 * 10^-^1^8 J\), \(1.02 * 10^-^1^7 J\)
The energy levels of an electron trapped in an infinite potential well are given by:
\(E_n = (n^2 h^2)/(8mL^2)\)
where n is the quantum number, h is Planck's constant, m is the mass of the electron, and L is the width of the potential well.
Case 1: L = 0.10 nm
For n = 1
\(E_1 = (1^2 * (6.626 * 10^-^3^4 J s)^2)/(8 * 9.109 * 10^-^3^1 kg *(0.10 * 10^-^9 m)^2) =\) \(1.64 * 10^-^1^8 J\)
Similarly for n = 2
\(E_2 = 6.57 * 10^-^1^8 J\)
\(E_3 = 1.48 * 10^-^1^7 J\)
\(E_4 = 2.63 * 10^-^1^7 JE_5 = 4.11 * 10^-^1^7 J\)
Therefore, the first five energy levels of an electron trapped in an infinite potential well with a width of 0.10 nm are \(1.64 * 10^-^1^8 J, 6.57 * 10^-^1^8 J, 1.48 * 10^-^1^7 J, 2.63 * 10^-^1^7 J,\) and \(4.11 * 10^-^1^7 J.\)
Case 2: L = 0.20 nm
\(E_1\) = \((1^2 * (6.626 * 10^-^3^4 J s)^2)/(8 * 9.109 * 10^-^3^1 kg * (0.20 * 10^-^9 m)^2)\) =\(4.11 * 10^-^1^9 J\)
\(E_2\) = \(1.64 *10^-^1^8 J\)
\(E_3\) = \(3.70 * 10^-^1^8 J\)
\(E_4\) = \(6.58 * 10^-^1^8 J\)
\(E_5\) = \(1.02 * 10^-^1^7 J\)
Therefore, the first five energy levels of an electron trapped in an infinite potential well are \(4.11 * 10^-^1^9 J\), \(1.64 *10^-^1^8 J\), \(3.70 * 10^-^1^8 J\), \(6.58 * 10^-^1^8 J\), \(1.02 * 10^-^1^7 J\).
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Related Questions
what is the difference between the acceleration of his head and feet if the astronaut is 2.00 m tall?
Answers
The difference between the acceleration of his head and feet is 27.745 m/s².
What is Acceleration?Acceleration of an object is the rate of change of the velocity of an object with respect to the time taken. Acceleration is a vector quantity. The orientation of an object's acceleration is given by the orientation of the net force which is acting on that object.
a. The center seeking acceleration of a body is known as centripetal acceleration. The expression is given as,
a = v²/ r
v = \(\sqrt{ar}\)
v = \(\sqrt{12.5g X 8.84}\)
v = \(\sqrt{12.5g X 9.8 X 8.84}\)
v = 32.92 m/s
Thus, the maximum speed of the astronaut's head is 32.92 m/s.
b. With difference in length between the head and feet, the new length is,
r' = 8.84 - 2.00 = 6.84 m
Then the difference in acceleration is,
a' = a - a''
a'' is the acceleration of astronaut. And its value is,
a'' = ω² × r'
a'' = a/r × r'
a'' = (12.5g/ 8.84) × 6.84
a'' = (12.5×9.8/ 8.84) × 6.84
a'' = 94.88 m/s²
Then, the difference in acceleration is,
a' = 12.5g - 94.88
a' = 12.5×9.8 - 94.88
a' = 27.745 m/s²
Thus, the required difference between the acceleration of the head and the feet of astronaut is 27.745 m/s².
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Your question is incomplete, most probably the complete question is:
At its Ames Research Center, NASA uses its large 20-G centrifuge to test the effects of very large accelerations (hypergravity) on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and the astronaut is strapped in at the other end. Suppose that he is aligned along the arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this machine is typically 12.5 g .Part A How fast must the astronaut's head be moving to experience this maximum acceleration?Part B What is the difference between the acceleration of his head and feet if the astronaut is 2.00 m tall?
The Mechanical Advantage equation is written as ___
Answers
MA = Fo/Fi
In this lab, you will use a falling cylinder attached to a
propeller in a water bath to explore the conversion of
energy in a system. You will vary two different variables
and determine how each one affects the temperature of
the water. In the space below, write a scientific question
that you can answer by doing this experiment.
Answers
In a lab, while performing the experiment, one question that I will ask will be - How potential energy can be converted into thermal energy? The answer for tat will be by seeing and understanding the sample response in the experiment.
What separates potential energy from thermal energy?Potential energy is released from them when they are divided. A particle's potential energy increases with distance. As they gain speed, their kinetic energy increases. The thermal energy of an object is the sum of the kinetic and potential energies of all the particles.
What gives thermal energy its potential?Energy from heat transfer as potential and kinetic energy
This occurs as a result of the attractive forces they generate for one another. Additionally, the particles are forced apart by a rise in body temperature. As a result, as their potential energy rises, so do the forces of attraction between them.
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Suppose you lift a stone that has a mass of 5.3 kilograms off the floor onto a shelf that is 0.5 meters high. How much work have you done
Answers
I have done a total of 5.4 joules of work when I lifted a stone with a mass of 5.3 kilograms off the floor onto a shelf 0.5 meters high.
To determine the amount of work done in lifting the stone onto the shelf, we can use the equation:
Work = Force × Distance
In this case, the force required to lift the stone is equal to its weight, which can be calculated using the formula:
Weight = Mass × Acceleration due to gravity
The mass of the stone is given as 5.3 kilograms. The acceleration due to gravity on Earth is approximately 9.8 meters per second squared.
So, the weight of the stone is:
Weight = 5.3 kg × 9.8 m/s²
Next, we need to calculate the distance over which the stone was lifted. The height of the shelf is given as 0.5 meters.
Now, we can substitute these values into the work equation:
Work = Force × Distance
Work = Weight × Distance
Work = (5.3 kg × 9.8 m/s²) × 0.5 m
Work = 5.4J.
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Mangrove forests play an important role in _______.
a.
fisheries
b.
coastal protection
c.
wildlife habitat
d.
all of the above
Please select the best answer from the choices provided
A
B
C
D
Answers
At high tide fish will feed among the mangrove roots - rich fishing ground
The trees trap sediment and soil in the river that would flow out to sea which also helps stop erosion
Wildlife utilise almost every part of the tree, with insects and birds, monkeys and lizards in the branches, shrimps and fish in the roots, and snails and clams in the soil
6th grade science I mark as brainliest.
Answers
Answer:
Solution:-Distance =400m
Time=20s
We need to find speedAs we know that
\({\boxed{\sf speed \dfrac {Distance {}_{(d)}}{Time {}_{(t)}}}}\)
Substitute the values\(\LARGE\leadsto\sf speed=\dfrac {400}{20}\)
\(\LARGE\leadsto\sf 20m/s\)
What is the name of the wires that connect the light bulb and the potato? in the potato lighting up the bulb experiment.
Answers
Answer:
Potato battery or Vegetable battery
Explanation:
Using a potato to light up a light bulb is an example of an experiment in which chemical energy is converted into electrical energy. This process is called a potato battery or a vegetable battery. It works by creating a simple electrical circuit between two electrodes (usually copper and zinc electrodes) inserted into the potato. The potato acts as an electrolyte, allowing charged ions to move between the two electrodes, generating an electric current that can be used to power a small device like a light bulb.
The potato battery is often used as an educational tool to demonstrate the basic principles of electricity and energy conversion.
What is a gene?
A.
A segment of a protein
B.
A segment of a DNA molecule
C.
A series of amino acids
D.
A series of DNA molecules
Answers
Answer:B. A segment of a DNA molecule
Explanation:
Two trains leave a station at the same time, Train A travels at a constant speed of 16 m/s. Train B starts at 8.0 m/s but accelerates constantly at 1.0 m/s squared. After 10.0 seconds, which train has the greater speed?
Answers
Answer:
Train B
Explanation:
train a is traveling at 16m/s no matter what time since it's a constant
to find final velocity of train B we use
v2=v1 +at
v1 = 8m/s
a = 1m/s squared
t = 10 s
v2 = 8 + 1(10)
v2 = 18
train B travelling at 18 m/s at 10 secs
the half-life of iodine-123 is 13.3 hours. how much of a 25.0 mg sample will remain after 39.9 hours?
Answers
3.12 mg of sample will remain after 39.9 hours if the half life of iodine is 13.3 hours.
What does half-life mean?Half life of the process is the time necessary for the reaction rate to fall to one-half its original amount. A statistic that is connected to the reaction's rate constant is the split of a first-order order reaction.
Briefing:
Given, Half life of iodine is 13.3 hours. so,
Half life t1/2 = ln 2/ K
k = 0.693 / t1/2
= 0.693 /13.3 hours
= 5.21 *10-2
The flow time is based on rate law which would be different for each emotions. A first-order interaction is one in which only one reactant's concentration affects the rate of the reaction. As a result, it is sometimes referred to as a unimolecular reaction. For this kind of reaction, the rate equation is: The first order reaction's rate constant is,
k= 1/t ln [A]0 / [A]t
t = 39.9 hours
k = 5.21 * 10-2 / hour
putting all the values in the expression of rate constant for first order reaction we get,
[A]t = 3.12mg
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which statement regarding a short circuit is true? group of answer choices a short circuit is an accidental low-resistance connection in a circuit, typically when the power is connected directly to ground. a short circuit happens when a circuit is broken or interrupted a short circuit happens when the resistance in a circuit is too low a short circuit is dangerous because it creates a build-up of static charge
Answers
The correct statement regarding a short circuit is that it is an accidental low-resistance connection in a circuit, typically when the power is connected directly to ground.
A short circuit occurs when current flows through an unintended path with low resistance, bypassing the normal load.
This can cause excessive current flow, overheating, and potential damage to the circuit or even start a fire.
It is important to note that a short circuit can be dangerous and should be addressed immediately to prevent any harm.
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Should Fast Food Companies be held responsible for the obesity problem in the US or any country? Why?
Answers
a disc rotates at 870 rpm (revolutions per minute). what is the angular speed (in rad/s)?
Answers
Angular speed is the rate of change of angular displacement with respect to time. It is measured in radians per second (rad/s).
To convert from revolutions per minute (rpm) to radians per second, we need to use the following formula:
angular speed (in rad/s) = angular speed (in rpm) x 2π/60
where 2π is the number of radians in a full circle (360 degrees) and 60 is the number of seconds in a minute.
Using this formula, we can find the angular speed of the disc that rotates at 870 rpm as follows:
angular speed (in rad/s) = 870 x 2π/60angular speed (in rad/s) = 870 x 0.10472
angular speed (in rad/s) = 91.1
Therefore, the angular speed of the disc that rotates at 870 rpm is 91.1 rad/s.
To calculate the angular speed in rad/s, we'll first convert the given rotational speed from rpm to revolutions per second and then multiply by 2π to obtain the angular speed in radians per second.
Given: 870 rpm
Step 1: Convert rpm to revolutions per second (rps)
870 rpm ÷ 60 = 14.5 rps
Step 2: Convert rps to rad/s
Angular speed = 14.5 rps × 2π rad/revolution
Angular speed ≈ 91 rad/s
So, the angular speed of the disc is approximately 91 rad/s.
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Which force is most important inside an atom?
O A. Gravity
O B. Air resistance
O C. Friction
O D. Strong nuclear force
Answers
Answer:
D- fuerza nuclear fuerte
Explanation:
A hot air balloon pilot is choosing a day and time to launch her new balloon. Table 1 shows the weather forecast for the next three days.
Temperature at 6 a.m. (°C). Temperature at 12 p.m. (°C). Temperature at 6 p.m. (°C)
Monday. 4. 18. 22
Tuesday. 6. 19. 24
Wednesday. 10. 20. 25
If the pilot wants to rise as high as possible while using as little fuel as possible, on which day should she launch her balloon? Explain your answer.
Answers
The balloon will rise the most on Wednesday due to high temperature that will increase the thermal energy of the balloon and cause it to rise higher.
Average daily temperatureThe average daily temperature of the different days is calculated as follows;
Monday = (4 + 18 + 22)/3 = 14.67 ⁰C
Tuesday = (6 + 19 + 24)/3 = 16.3 ⁰C
Wednesday = (10 + 20 + 25)/3 = 18.3 ⁰C
The average daily temperature of Wednesday is the greatest.
The balloon will rise the most on Wednesday due to high temperature that will increase the thermal energy of the balloon and cause it to rise higher.
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State two properties of magnetic lines of force.
Answers
The magnetic lines of force has the following properties:
Each line is a closed and continuous curve.
They originate from the north pole and terminate at the south pole.
They will never intersect each other.
They are crowded near the poles where the magnetic field is strong
If a 4500 kg car is traveling with an acceleration of 35.2 m/s/s, what is the force acting on it?
Answers
Answer:
158,400 JExplanation:
The force acting on an object given it's mass and acceleration can be found by using the formula
force = mass × acceleration
From the question we have
force = 4500 × 35.2 = 158400
We have the final answer as
158,400 JHope this helps you
Use the drop-down menus to complete the statements. Outlook allows users to insert symbols and characters not located on the , but they can have shortcut keys. Inserting horizontal lines in the message body breaks up different sections and mostly benefits people using Outlook on .
Answers
Answer:
Keyboard and Mobile devices
Explanation:
got it right on edge 2021
Answer:
Outlook allows users to insert symbols and characters not located on the
keyboard
, but they can have shortcut keys.
Inserting horizontal lines in the message body breaks up different sections and mostly benefits people using Outlook on
mobile devices
.
Explanation:
Light passes straight through two vertical polarizers. The axes of the filters are aligned parallel to each other. How does the light that passes through the second filter compare to the light that passed through the first filter?.
Answers
The direction of the polarized light after passing the first and the second filter are the same, however the intensity of the light after passing the first and second polarizer are half and fourth of its original intensity, respectively.
Light polarization is a filter of electromagnetic waves such that it propagates into one transmission axis only.
When light passes through a polarizer, its intensity will decrease by half.
Suppose the intensity of unpolarized light is I₀, after passing the first polarizer, its intensity becomes:
I₁ = 1/2 . I₀
After passing the second polarizer, the intensity will further decrease by half, or:
I₂ = 1/2 . I₁
I₂ = 1/2 .1/2 . I₀ = 1/4. I₀
Since both polarizers are vertical filters, then the direction of the polarized light after passing the first and the second filter are the same.
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Radio waves travel at the speed of light. marsha listens to a radio station at 91.3 mhz., which is a frequency of hz. what is the wavelength of this radio signal in a vacuum?
Answers
The wavelength of the radio signal at 91.3 MHz is approximately 3.28 meters.
Radio waves are a type of electromagnetic radiation that travel at the speed of light in a vacuum, which is approximately 299,792,458 meters per second. The relationship between the frequency (f) and the wavelength (λ) of a wave is given by the formula:
λ = c / f
Where:
λ = wavelength
c = speed of light
f = frequency
In this case, we are given the frequency of the radio signal as 91.3 MHz. To calculate the wavelength, we need to convert the frequency to hertz (Hz) by multiplying it by 1 million (since 1 MHz equals 1 million Hz). Therefore, the frequency in Hz would be 91,300,000 Hz.
Substituting the values into the formula:
λ = 299,792,458 m/s / 91,300,000 Hz
Simplifying the expression:
λ ≈ 3.28 meters
Therefore, the wavelength of the radio signal at 91.3 MHz is approximately 3.28 meters.
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how to solve resultant of two forces when given an angle
Answers
Answer:
Explanation:
To find the resultant of two forces when given an angle, you can use the two-dimensional vector addition method. Here are the steps to follow:
Represent each force as a vector. The magnitude of each vector should be equal to the magnitude of the force, and the direction of each vector should be equal to the direction of the force.
Place the vectors on a coordinate plane with their tails at the origin and their tips pointing in the direction of the forces.
Find the x and y components of each vector using trigonometry. For example, if the angle between the x-axis and the vector is θ, then the x-component of the vector is equal to the magnitude of the vector times cos(θ) and the y-component of the vector is equal to the magnitude of the vector times sin(θ).
Add the x and y components of the two vectors to find the x and y components of the resultant vector.
Use the Pythagorean theorem to find the magnitude of the resultant vector. The magnitude of the resultant vector is equal to the square root of the sum of the squares of the x and y components.
Find the direction of the resultant vector by finding the inverse tangent (tan^-1) of the ratio of the y-component of the resultant vector to the x-component of the resultant vector.
The final result is the vector that starts at the origin and ends at the point determined by the x and y components of the resultant vector, with a magnitude equal to the magnitude of the resultant vector and a direction equal to the direction of the resultant vector.
By using this method, you can find the magnitude and direction of the resultant of two forces given an angle between them.
Using the Skygazer's Almanac for 2022 at 40 degrees.
What day will Venus and Saturn be in opposite parts of the sky
this year?
Answers
According to the Skygazer's Almanac for 2022 at 40 degrees, Venus and Saturn will be in opposite parts of the sky on December 17, 2022.
The Skygazer's Almanac provides astronomical information for a specific location and year. In this case, at a latitude of 40 degrees, the almanac indicates that Venus and Saturn will be in opposite parts of the sky on December 17, 2022. This means that Venus and Saturn will appear at opposite sides of the celestial sphere as observed from Earth. However, it's important to note that the almanac's predictions are approximate and can be influenced by various factors, including atmospheric conditions and the observer's specific location. To obtain the most accurate and up-to-date information, it is recommended to consult more recent astronomical sources or use specialized software that can provide precise positions and dates for celestial events.
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A road zig-zags every 100m, first to the East, then to the North ten times. How apart are these two ends?
Answers
Given:
Length of each road before it zig-zags = 100 m
Number of tmes = 10
Let's find the distance between the two ends of the roads.
Let's first make a free sketch of the road.
To find the distance between the ends of one zig-zag, apply Pythagoean theorem:
\(\begin{gathered} L=\sqrt{(100*10)^2+(100+10^2)} \\ \\ L=\sqrt{(1000)^2+(1000)^2} \end{gathered}\)Solving further:
\(\begin{gathered} L=\sqrt{1000000+1000000} \\ \\ L=\sqrt{2000000} \\ \\ L=1414.21\text{ m} \end{gathered}\)Therefore, the distance between both ends is 1414.12 m.
• ANSWER:
1412.12 m
What is one property of a suspension that is different from that of a solution or a colloid?
a) If left to rest, the particles of a suspension will settle out.
B) A suspension is always clear
C) The particles of a colloid will settle out.
d) Suspensions are colorless
Answers
Answer:
A
Explanation:
If left to rest it will separate.
explain liquid -liquid extraction
Answers
Answer:
Explanation: Liquid–liquid extraction (LLE), also known as solvent extraction and partitioning, is a method to separate compounds or metal complexes, based on their relative solubilities in two different immiscible liquids, usually water (polar) and an organic solvent (non-polar).
What quality differentiates hydrogen (H) from the other elements in group 1, the alkali metals?
a. It has more than one valence electron.
b. It is found by itself in nature.
c. It is not very reactive.
D. It is a non-metal.
Answers
Answer:
D. It is a non-metal.
A 4.0×1010kg asteroid is heading directly toward the center of the earth at a steady 32 km/s. To save the planet, astronauts strap a giant rocket to the asteroid perpendicular to its direction of travel. The rocket generates 5.0×109N of thrust. The rocket is fired when the asteroid is 4.0×106km away from earth. You can ignore the earth’s gravitational force on the asteroid and their rotation about the sun.
Answers
Where is ozone considered a pollutant? a. In the stratosphere where it blocks the sun's rays b. In the mid-atmosphere where it prevents cloud formation. C. In the troposphere where it impairs normal lung function. d. It is a pollutant everywhere it is found.
Answers
C. In the troposphere where it impairs normal lung function.
An observer sitting at a bus stop sees the bus drive by at 30 m/s to the east. He also sees a
passenger on the bus walking to the back at 2 m/s. What is the passenger's velocity relative
to the bus?
Answers
Answer:
32 m/s
Explanation:
The speed of a bus is 30 m/s due East wrt the passenger
He also sees a passenger on the bus walking to the back at 2 m/s.
We need to find the passenger's velocity relative to the bus. As the observer sees that the bus and the passenger are moving in opposite direction. Let v is the relative velocity. So,
v = 30 m/s + 2 m/s
v = 32 m/s
Hence, the passenger's velocity relative to the bus is 32 m/s.
Does earths gravitational force field act on objects that aren’t touching earths surface?
( Explanation needed ASAP NEEDED
Answers
Answer:
no the earth gravitational force field
Answer:
yes, it acts on everything within the earth
Explanation: