λ quantum particle of mass m is placed in a onedimensional box of length L . Assume the box is so small that the particle's motion is relativistic and K= P² / 2 m is not valid. (b) Assume the particle is an electron in a box of length L=1.00 \times 10^{-12} \mathrm{~m} . Find its lowest possible kinetic energy.
Answers
The lowest possible kinetic energy of an electron in a one-dimensional box of length L = 1.00 × 10^(-12) m is approximately 4.33 × 10^(-12) J.
For a one-dimensional box of length L, the energy levels for a particle of mass m are given by:
E_n = (n^2 * h^2) / (8mL^2)
Where:
h = Planck's constant
n = quantum number
m = mass of the particle
L = length of the box
To find the lowest possible kinetic energy when the particle is an electron in a box of length L = 1.00 × 10^(-12) m, we need to find the energy of the ground state or first energy level by setting n = 1:
E_1 = (1^2 * h^2) / (8mL^2)
Substituting the values into the above expression, we get:
E_1 = (1^2 * (6.626 × 10^(-34) Js)^2) / (8 * (9.11 × 10^(-31) kg) * (1.00 × 10^(-12) m)^2)
Simplifying the expression, we find:
E_1 = 4.33 × 10^(-12) J
The total energy of the particle in the box is given by:
E = mc^2 + E_k
Where:
m = mass of the particle
c = speed of light
E_k = kinetic energy of the particle
Substituting the value of the mass of the electron and the lowest possible kinetic energy of the electron, we get:
E = (9.11 × 10^(-31) kg) * (2.998 × 10^8 m/s)^2 + 4.33 × 10^(-12) J
Simplifying the expression, we find:
E = 4.10 × 10^(-10) J
Therefore, the lowest possible kinetic energy of an electron in a one-dimensional box of length L = 1.00 × 10^(-12) m is approximately 4.33 × 10^(-12) J.
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Related Questions
A projectile is fired with an initial speed of 150 m/s at an angle of 47 degrees above the horizontal. Determine the velocity of the projectile 2seconds after firing. Determine the total time in the air. Determine the maximum height reached by the projectile.
Answers
The maximum height reached by the projectile is approximately 283.13 meters.
To determine the velocity of the projectile 2 seconds after firing, we need to break down the initial velocity into its horizontal and vertical components.
The horizontal component remains constant throughout the motion, so it will be the same as the initial velocity: 150 m/s.
For the vertical component, we can use the equation v = u + at, where v is the final velocity, u is the initial vertical velocity component, a is the acceleration due to gravity (-9.8 m/s^2), and t is the time.
Since the projectile is fired upwards, the initial vertical velocity component is given by u = u_initial * sin(angle), where u_initial is the initial velocity (150 m/s) and the angle is 47 degrees.
Using this information, we can calculate the vertical velocity component at t = 2 seconds:
v = u + at
v = (u_initial * sin(angle)) + (a * t)
v = (150 * sin(47)) + (-9.8 * 2)
v ≈ 76.65 - 19.6
v ≈ 57.05 m/s
So, the velocity of the projectile 2 seconds after firing is approximately 57.05 m/s.
To determine the total time in the air, we need to find when the projectile returns to the same height from which it was launched. The total time in the air can be calculated using the equation t = (v_final - u_initial * sin(angle)) / (-a), where v_final is the final vertical velocity component (0 m/s).
0 = (u_initial * sin(angle)) + (-9.8 * t_total)
t_total = (u_initial * sin(angle)) / 9.8
Using the given values, the total time in the air is approximately:
t_total = (150 * sin(47)) / 9.8
t_total ≈ 6.42 seconds
So, the total time in the air is approximately 6.42 seconds.
To determine the maximum height reached by the projectile, we can use the equation h_max = (u_initial^2 * sin^2(angle)) / (2 * a), where h_max is the maximum height.
h_max = (150^2 * sin^2(47)) / (2 * 9.8)
h_max ≈ 283.13 meters
Therefore, the maximum height reached by the projectile is approximately 283.13 meters.
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0
What is 33 C in absolute temperature? hs
Answers
Answer:
33 Celsius is 306.15 in absolute temperature
range, variance, and standard deviation are measurements of: a. gradations of quality. b. sampling error. c. intensity. d. dispersion. e. quantity
Answers
The terms range, variance, and standard deviation are measurements of dispersion (option d). Dispersion refers to the extent to which data points are spread out or clustered together in a distribution.
Range, variance, and standard deviation are all measurements of dispersion in a set of data. Dispersion refers to the degree to which the data points in a set are spread out from each other.
Range is the simplest measure of dispersion and is calculated by subtracting the minimum value from the maximum value in the set. Variance is a more detailed measure of dispersion and is calculated by taking the average of the squared differences between each data point and the mean of the set. Standard deviation is the square root of the variance and is used as a more easily interpretable measure of dispersion.In summary, range, variance, and standard deviation are all measures of the spread of data in a set. They tell us how much the data points vary from each other and give us a sense of the overall variability of the data. These measures are important in statistical analysis because they can help us understand the distribution of data and make informed decisions based on that understanding.Know more about the measure of dispersion
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Using what you have learned about series and parallel circuits, explain how some appliances in your kitchen receive power while others do not. (PLEASE HELPP)
Answers
To learn series and parallel circuits, to know the some appliances in your kitchen receive power while others do not.
What is series circuits?
A series circuit is an easy way for electrons to travel to one or more resistors. Anything that depends on a cell for power is a resistor. A bulb frequently serves as the resistor in a series circuit.
What is parallel circuit?
Branching is used in a parallel circuit so that the current is divided and only a portion of it passes through each branch. In a parallel circuit, the voltage, or potential difference, across each branch is the same, but the currents may differ.
While plugged in, a range of various electronic equipment and appliances, such as televisions, toasters, lamps, and more, can use electricity even when they're off.
Therefore, known the series and parallel circuits, the some appliances receive powers.
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What are water droplets that act as a prism?
O a
Ob
OC
Od
mirage
rainbow
filter
concave mirror
Answers
Water droplets that act as prism are phenomenon known as : b) rainbow.
What are water droplets that act as prism?When light enters water droplet and is refracted, it is dispersed into its component colors due to difference in the index of refraction of each color of light. This results in band of colors in the shape of arc with red on outer edge and violet on inner edge, with other colors of spectrum in between. This is the same effect as prism which disperses light in the same way.
Rainbows appear in seven colors because water droplets break sunlight into seven colors of spectrum and you get the same result when sunlight passes through prism. Water droplets in the atmosphere act as prism though traces of light are very complex.
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What do all electromagnetic waves have in common?
• They can travel at the speed of light
o They has the same wavelengths.
O They travel only through matter
O They have nonmoving magnetic fields
Answers
Can the sun explain global warming? ( 2 points) Suppose that the Earth has warmed up by 1 K in the last hundred years. i) How much would the solar constant have to increase to explain this? ii) Compare this to the observed fluctuation of the solar constant over the past 400 years (shown in class) For part (i), begin with the standard 'blackbody' calculation from class, that is: set α=0.30, and assume that the Earth acts as a blackbody in the infrared.
Answers
No, the sun cannot explain global warming. Global warming is a phenomenon in which the temperature of the Earth's surface and atmosphere is rising continuously due to human activities such as deforestation, burning of fossil fuels, and industrialization.
This increase in temperature cannot be explained only by an increase in solar radiation.There are several factors which contribute to global warming, including greenhouse gases such as carbon dioxide, methane, and water vapor. These gases trap heat in the Earth's atmosphere, which causes the planet's temperature to rise. The sun's radiation does contribute to global warming, but it is not the main cause.
i) To calculate the increase in solar radiation that would cause the Earth to warm up by 1 K, we can use the following formula:ΔS = ΔT / αWhere ΔS is the increase in solar constant, ΔT is the increase in temperature, and α is the Earth's albedo (reflectivity).α = 0.30 is the standard value used for the Earth's albedo.ΔS = ΔT / αΔS = 1 K / 0.30ΔS = 3.33 W/m2So, to explain the increase in temperature of 1 K over the last hundred years, the solar constant would need to increase by 3.33 W/m2.
ii) The observed fluctuation of the solar constant over the past 400 years has been around 0.1% to 0.2%. This is much smaller than the 3.33 W/m2 required to explain the increase in temperature of 1 K over the last hundred years. Therefore, it is unlikely that the sun is the main cause of global warming.
The sun cannot explain global warming. While the sun's radiation does contribute to global warming, it is not the main cause. The main cause of global warming is human activities, particularly the burning of fossil fuels, which release large amounts of greenhouse gases into the atmosphere.
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which of the following planets has the least substantial atmosphere? group of answer choicesA. marsB. venusC. mercuryD. earthE. neptune
Answers
A
Mercury has the least substantial atmosphere among the given planets.
Mercury, the closest planet to the Sun, has a very thin and tenuous atmosphere. Its atmosphere consists mainly of atoms and molecules that have been blasted off its surface by the solar wind, rather than being generated from internal processes like on Earth. The atmosphere on Mercury is extremely sparse, with a surface pressure about 1 trillion times lower than Earth's atmospheric pressure.
Due to its weak gravitational pull, Mercury is unable to retain a significant atmosphere compared to other planets in the list.Among the given options, Mercury has the least substantial atmosphere
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The center of the atom is
Answers
Answer:
The nucleus (center) of the atom contains the protons (positively charged) and the neutrons (no charge). The outermost regions of the atom are called electron shells and contain the electrons (negatively charged).
Explanation:
what are the example of ultraviolet rays
Answers
1. Sunlight: The sun is the primary natural source of UV rays. UV radiation from the sun is responsible for causing sunburn, skin aging, and an increased risk of skin cancer.
2. Tanning beds: Tanning beds and sun lamps emit UVA and UVB radiation, which can also cause skin damage and increase the risk of skin cancer.
3. Fluorescent lights: Some types of fluorescent lights emit small amounts of UV radiation.
4. Welding torches: Welding torches emit high levels of UV radiation, which can cause eye damage and skin burns if protective gear is not worn.
5. Germicidal lamps: These lamps are used to disinfect surfaces and air, but can also emit UVC radiation, which is harmful to living organisms and can cause skin and eye damage.
arrange the following types of electromagnetic radiation in order of increasing wavelength: ultraviolet light, radio waves, microwaves
Answers
The electromagnetic radiation in order of increasing wavelength is ultraviolet light < microwaves < radio waves.
The wavelength range of the given waves are as follows:
Ultraviolet light = 400 nm to 1 nmMicrowaves = 1 mm to 25 μmRadio waves = > 1 mmWavelength is the distance between identical points in the adjacent cycles of a waveform signal propagated in space. The identical points means either two crests or two troughs. It is measured in the direction of the wave.
Therefore, in terms of wavelength ultraviolet light < microwaves < radio waves.
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We observe a glowing cloud of gas in space with a spectroscope. We note that many of the familiar lines of hydrogen that we know on Earth seem to be in a different place. They are shifted toward the blue or violet end of the spectrum compared to their positions in the spectrum of glowing hydrogen gas on Earth. From this we can conclude that: Group of answer choices the cloud is moving away from us the cloud is much hotter than hydrogen on Earth the cloud is moving toward us No information can be concluded from this observation alone the cloud is much cooler than hydrogen on Earth
Answers
Answer:
No information can be concluded from this observation alone the cloud is much cooler than hydrogen on Earth
A ball is thrown upward at time t=0 from the ground with an initial velocity of 60 m/s (~ 134 mph). Assume that g = 10 m/s^2. at what time t does the ball reach the ground?
Answers
According to the statement, on the ball thrown upward from the ground, it will reach the ground at time t=12 seconds.
The ball will reach the ground at time t when its vertical displacement is zero. We can use the equation for vertical displacement, \(y = v0t - (1/2)gt^2\), where v0 is the initial velocity, g is the acceleration due to gravity, and t is the time. Plugging in the given values, we get:
\(0 = 60t - (1/2)(10)t^2\)
Rearranging the equation and factoring out t, we get:
t(60 – 5t) = 0
This gives us two possible values for t: 0 and 12 seconds. Since the ball is thrown at t=0, the time when it reaches the ground is t=12 seconds.
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The inventor of the electric cell was:
O Coulomb
Franklin
o Gilbert
O Volta
Answers
Answer:
The inventor of the electric cell was:
Alessandro Volta (in other words, Volta)
Explanation:
Answer:
Volta
Hope this helped you!!
Brainliest plsss
Explanation:
Alessandro Volta, in full Conte Alessandro Giuseppe Antonio Anastasio Volta, (born February 18, 1745, Como, Lombardy [Italy]—died March 5, 1827, Como), Italian physicist whose invention of the electric battery provided the first source of continuous current
All systems move from high pressure to low pressure. (T or F)
Answers
Answer:
pun
Explanation:
Which two types of energy does an apple falling to the ground have?
Answers
Answer: kinetic energy and potentoal
Explanation: dhsjsjdne
please answer of of them.
Answers
Answer:
1. 7.5 km/h
2. 1 hour, 52 minutes, 30 seconds
3. 0.8 Joules
4. 13.33 mph
5. 19456 Joules
6. 10.5 kg
Explanation:
Four states of matter and describe the particles arrangement of each
Answers
Answer:
There are four natural states of matter: Solids, liquids, gases and plasma.
Explanation:
The fifth state is the man-made Bose-Einstein condensates. In a solid, particles are packed tightly together so they don't move much.
An ocean scientist plans to spend several days underwater in a submarine. Doctors on land will monitor her body to make sure she is healthy during her trip. What is one way doctors will be able to tell whether her body is healthy enough to do all her tasks while she is in the submarine?
Answers
Answer:
The doctors could see if her cells are getting the molecules they need from food and air
Explanation:
The doctors could see if her cells are getting the molecules they need from food and air. Doing so allows the doctors a general overview of how well her body's biological systems are performing since the basic necessities of the human system are food and oxygen. Therefore if the body is receiving both food and oxygen properly and distributing it properly and efficiently as well without any problems then the most likely outcome is that she is healthy enough to perform her tasks in the submarine under more pressure.
Answer:
The doctors could see if her cells are getting the molecules they need from food and air
Explanation:
plzs help me asap!!!!!
Directions: Write a T in the blank for True, or an F for False.
6. Newton's First Law states that every action has an equal/opposite reaction.
7. Newton's Second Law can be simplified to F=ma.
8. An object will move in the same direction as the unbalanced force acting upon it.
9. Friction always acts in the same direction as the motion of the object.
10. If there is no next force acting on an object, that means in ALL SITUATIONS that the object will not move.
Answers
Answer:
6. False 7. True 8. False (Unbalanced forces acting upon an object changes the object's motion) 9. False 10. True (I'm not 100% sure if these answers are right though.)
Answer:
I confirm that answer LOL
Explanation:
who discovered that the earth revolves around the sun
Answers
Answer:
Nicolaus Copernicus
Explanation:
In 1543, Nicolaus Copernicus detailed his radical theory of the Universe in which the Earth, along with the other planets, rotated around the Sun. His theory took more than a century to become widely accepted.
while a rock thrown upward at 50 degrees to the horizontal rises, neglecting air drag, its horizontal component of velocity remains unchanged. decreases. increases.
Answers
While a rock thrown upward at 50 degrees to the horizontal rises, neglecting air drag, its horizontal component of velocity remains unchanged.
The horizontal component of velocity refers to the velocity in the horizontal direction, which is perpendicular to the vertical direction of the rock's motion. Neglecting air drag means that no external force acts on the horizontal component of velocity. According to Newton's first law of motion, an object in motion will continue to move at a constant velocity in the absence of external forces.
In this case, as the rock rises vertically, its horizontal component of velocity remains unaffected by the vertical motion. The force of gravity acts vertically downward and does not affect the horizontal motion of the rock. Therefore, the horizontal component of velocity remains unchanged throughout the rock's upward trajectory.
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When the normal force, (i.e., friction), is ________________ the shear force, the block moves downslope.
Answers
When the normal force, which is essentially friction, is less than the shear force, the block will start to move downslope.
In other words, the force pushing the block downslope (the shear force) becomes greater than the force pushing back against it (the normal force or friction).
This can occur due to a variety of factors, such as the incline of the slope, the weight of the block, and the surface properties of both the block and the slope.
Once the shear force overcomes the normal force, the block will start to slide down the slope, increasing in velocity until the forces are balanced again.
This concept is essential in understanding the mechanics of sliding and friction, and is commonly used in the fields of physics and engineering.
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you stretch a spring ball system 0.248 m away from its equilibrium point and watch it oscillate. you find that the system's angular frequency is 6.88 rad/sec. what is the maximum speed of the ball?
Answers
The maximum speed of the ball in this spring ball system is 1.704 m/s.
To find the maximum speed of the ball in this spring ball system, we need to use the equation for the angular frequency (ω) of an oscillating system:
ω = √(k/m)
Where k is the spring constant and m is the mass of the ball. We can rearrange this equation to solve for k:
k = mω^2
Now that we have the spring constant, we can use the equation for the maximum velocity (vmax) of an oscillating system:
vmax = Aω
Where A is the amplitude of the oscillation, which in this case is 0.248 m. Substituting the values we have:
k = mω^2 = (m)(6.88 rad/sec)^2 = 299.8m
vmax = Aω = (0.248 m)(6.88 rad/sec) = 1.704 m/s
Therefore, the maximum speed of the ball in this spring ball system is 1.704 m/s.
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explain why EMF of a cell is greater than the potential difference across the cell when it is passing a current an external resistance
Answers
The EMF of a cell represents its maximum potential difference, while the potential difference across the cell when passing a current through an external resistance is reduced due to the internal resistance of the cell.
The electromotive force (EMF) of a cell refers to the maximum potential difference that the cell can provide when it is not connected to any external circuit. It is essentially the voltage produced by the chemical reactions occurring within the cell. On the other hand, the potential difference across the cell when it is passing a current through an external resistance is often lower than the EMF.
This difference in values can be attributed to the internal resistance of the cell. When a current is drawn from the cell, it encounters resistance within the cell itself due to factors such as the resistance of the electrolyte and the internal structure of the cell. This internal resistance causes a voltage drop within the cell, reducing the potential difference across the external circuit.
According to Ohm's Law (V = I * R), when current flows through a resistance (R), a voltage drop (V) occurs. In this case, the internal resistance of the cell causes a voltage drop within the cell itself. Hence, the potential difference across the external resistance is slightly lower than the EMF of the cell.
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The boat's 'echo sounder' could not be used in an aeroplane to measure its heigh
above the ground unless it had been modified.
Answers
True, this is because the echo sounder that is applicable to boats cannot be used directly for airplanes
How does an echo sounder work?By sending out sound waves and timing how long it takes for them to bounce back, an echo sounder, sometimes referred to as a sonar, is a device frequently used in boats to gauge the depth of the water beneath the craft.
When a sound pulse from an echo sounder strikes a solid item in the water, such as fish, vegetation, or other objects, the signal is reflected back to the surface.
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Which of these is an example of interference? A. two lasers pointing away from each other В. two different light waves colliding and adding together C. a light wave bending around the corner of an obstacle D. a light wave bouncing off of a flat surface
Answers
Answer:
I believe the answer is B. Although it might be C.
Explanation:
I hope this helps!
Consider a board meeting with n board members {1, 2, …, n}, each with a voting weight w_i (a positive integer) in the set W = {w_1, w_2, …, w_n}. When member i votes, their vote gets counted with weight w_i. A resolution being voted on by the board will pass if and only if the sum of the weights of `yes’ votes is a specific number T (a non-negative integer) – no more, no less.
Write an algorithm that will take as input the array W of weights (with w_i stored at index i) and the target sum T of voting weights and output TRUE if it is possible to pass a resolution with any combination of the input weights and FALSE otherwise. You may write the algorithm as pseudo-code or in a programming language of your choice
Answers
The required algorithm that will take as input the array W of weights (with w_i stored at index i) and the target sum T of voting weights and output TRUE if it is possible to pass a resolution with any combination of the input weights and FALSE otherwise is given below:
Algorithm: Function Can_Resolution_Passed (W, T)Initialize a Boolean variable Res with false.Set N as the length of array W. For i=1 to 2^N-1Iterate through the array W to find the sum of weights of the ith combination of the array W. Create a variable sum and initialize it with 0. For j=0 to N-1 If the jth bit of the binary representation of i is 1, then add W[j] to sum. End IfEnd For If sum is equal to T, then set Res to true and break the loop. End IfEnd ForReturn Res as the output.
End Function The above algorithm is checking all possible subsets of the array W, and for each subset, it is checking whether their sum is equal to the target sum T or not. If we get such a subset, then we return true, else we return false.The time complexity of the above algorithm is O(N*2^N), which is exponential.
But it is the best possible solution to the given problem because we need to check all possible subsets of the array W.
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A block on a horizontal surface of negligible friction is placed in contact with an ideal spring, as shown above. The block is moved to the left so that the spring is compressed a distance x from equilibrium and then released from rest. The block has kinetic energy k1 when it separates from the spring. When the spring is compressed a distance 2x and the block is released from rest, the kinetic energy of the block when it separates from the spring is:
Answers
Answer: 4K1
Explanation:
please help, i will mark brainliest.
Answers
The valid combinations are:
a) 5, 12, and 4b) 7, 7, and 7Total resistance for a circuit in series is R_T = R1 + R2 + R3 + ...
How to determine combinations and total resistance?Question 1
To determine the valid combinations of resistors for a circuit with a total resistance of 21, find combinations where the sum of the individual resistances equals 21. Analyze each option:
5, 12, and 4:
Total resistance = 5 + 12 + 4 = 21 (Valid combination)
7, 7, and 7:
Total resistance = 7 + 7 + 7 = 21 (Valid combination)
3, 3, and 3:
Total resistance = 3 + 3 + 3 = 9 (Invalid combination)
5, 5, and 5:
Total resistance = 5 + 5 + 5 = 15 (Invalid combination)
Therefore, the valid combinations are:
5, 12, and 4
7, 7, and 7
Question 2:
Regarding the second question, the equation that calculates the total resistance for a circuit in series is:
R_T = R1 + R2 + R3 + ...
So, the correct option is:
R_T = R1 + R2 + R3 + ...
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