The heat lost by one object is equal to the heat gained by the other.
What is heat?
heat is the energy that moves from one body to another when temperatures are different. Heat flows from the hotter to the colder body when two bodies with various temperatures are brought together. Usually, but not always, this energy transfer results in a rise in the temperature of a colder body and a fall in the temperature of a hotter body. By transitioning from one physical state (as well as phase) to another, such as from a phase from solid to liquid (melting), from the a solid to the a vapour (sublimation), from the a liquid to a vapour (boiling), either from one solid form to another, a substance can absorb heat without increasing in temperature.
This is because of the law of conservation of energy, which states that energy cannot be created or destroyed. As a result, the temperature of both objects will change until they reach the same equilibrium temperature. This is known as the law of thermal equilibrium, which states that the temperature of any two objects in thermal contact will eventually reach the same temperature.
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two capacitors of 4 μf and 8 μf are connected in parallel. what is the equivalent capacitance of this system?
The equivalent capacitance of this system is 12 micro F.
Let
C1 = 4 micro F
C2 = 8 micro F
C_parallel = C1 + C2
= 4 + 8
= 12 micro F
What is capacitance?
Capacitance is the ability of a component or circuit to collect and store energy in the form of electrical charge.
Capacitors are energy storage devices of various sizes and shapes. They consist of two sheets of conductive material (usually thin metals) sandwiched between insulators made of ceramic, foil, glass, or other material, or even air.
Insulators, also called dielectrics, increase the charging capacity of capacitors. Capacitors are sometimes called capacitors in the automotive, marine and aerospace industries.
The inner plate is connected to the two outer terminals. The outer terminal can be long and thin and resemble a small metal antenna or leg. These terminals can be plugged into a circuit.
Therefore, the equivalent capacitance of this system is 12.
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what evidence suggests that the protogalactic cloud that formed the milky way resulted from several collisions among smaller clouds?
The fact that the age and heavy element content of halo stars vary but do not appear to be correlated with the stars' distance from the galactic center indicates that the protogalactic cloud that gave rise to the Milky Way was the product of multiple collisions between smaller clouds .
How is it an indicating element?It makes plausible to think that the protogalactic cloud that gave birth to our Galaxy was nearly spherical given that the oldest stars, those in the halo and in globular clusters, are spread in a sphere of galaxy.Since the oldest stars in the halo are between 12 and 13 billion years old, we infer that the Galaxy first formed about that time.Other proof that galaxies in general started forming a bit more than 13 billion years ago can be found in the chapter on The Big Bang.The protogalactic cloud eventually condensed and created a thin revolving disk, much like in the case of star formation. Stars born before the cloud disintegrated did not take part in the disintegration, but have continued to orbit in the halo to the present day.Gas in the thin disk was broken up by gravitational forces into clouds or clumps with masses akin to star clusters. Later, these distinct clouds broke up even further to create stars.Due to the fact that the oldest stars in the disk are almost as old as the youngest stars in the halo, the collapse must have occurred quickly from an astronomical perspective, possibly taking only a few hundred million years.What are halo stars?The galaxy's outermost points, or halo stars, are simply regions where the imperium cannot spread since the astronomical's light does not shine. Several xenos races that the imperium has never encountered essentially make up its population.
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Oil is spilled from an oil rig in the Gulf of Mexico andspreads in a circle with the circumference changing at a rate of 40m/sec. How fast is the area of the spill increasing when thecircumference of the circle is 100Ï€ meters?
The area of the spill increasing when the circumference of the circle is 100π meters at a rate of 2000 sq. m/sec.
What is circumference ?The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.
The curve length around any closed figure is more often referred to as the perimeter. The term "circumference" can also refer to the circle's actual location, which corresponds to a disk's edge.
Given parameters:
circumference changing at a rate = 2π dr = 40m/sec.
the circumference of the circle is = 2πr = 100π meters
Hence, the rate of area of the spill increasing = 2πrdr
= 100π meters × 40m/sec/2π
= 2000 sq. m/sec.
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______require high temperatures and pressures to react with other elements.
Inert gases require high temperatures and pressures to react with other elements.
What are inert gases?A gas is considered to be inert if, under a specific set of circumstances, no chemical reactions occur. The noble gases, formerly known as the inert gases, frequently do not react with a wide variety of substances as argon and neon (at normal conditions).
Because they contain a fully filled valence shell and an electronic configuration of ns²np⁶, inert gases do not react with other chemicals.
As a result, they are referred to as noble gases and are in the periodic table's group 18.
But under high temperatures and pressures Inert gases react with other elements.
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the amount of heat necessary to change 1 kg of a liquid into a gas at the same temperature is called the
Latent heat of vaporisation is required for liquidation of bag per 1 kilogram.
What is latent heat of vapourisation?The amount of thermal energy produced when a gas condenses into a liquid or the amount needed for a liquid to evaporate into a gas is known as the latent heat of vaporization.
The enthalpy of vaporization is another name for the latent heat of vaporization. Steam burns are extremely harmful because of the high latent heat of vaporization that water has.
The energy required to change the state of 1 kg of a substance without affecting its temperature is known as the specific latent heat of that substance.
We can tell that the substance is being measured per unit mass due to the distinction from latent heat. Additionally, specific latent heat is a dense feature of matter because it is measured per unit mass.
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one end of a string is attached to a ball, with the other end held by a student such that the ball is swung in a horizontal circular path of radius r at a constant tangential speed. at a later time, the tension force exerted on the ball remains constant, but the length of the string is decreased to r4. what is the new tangential speed of the ball?
According to the given statement Half the original speed is the new tangential speed of the ball.
Why is it called tangential speed?Any item moving along the circular path has a linear component to its speed called tangential velocity. An object's velocity is always pointed tangentially when it travels in a circle at a distance rr from the center. Tangential velocity is the name given to this.
Is tangential speed a constant quantity?Although the tangential velocity vector's direction changes as the item spins, the tangential speed remains constant. Note that along the circular motion's radius vector, the centripital speed is constantly moving inward. Two vectors combine to form circular motion as one of their components. The first is when anything moves forward (the tangential velocity).
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hree uniform spheres fig. p13.45. (a) what are the mag- nitude and direction of the force on a 0.0150 kg particle placed at p? (b) if the spheres are in deep outer space and a 0.0150
a) the magnitude of the force on particle is 9.7 x 10⁻¹² N and direction is 45° counter clockwise.
b) if spheres are in outer space of 0.0150, then velocity will be 3 x 10⁻⁵ km/s
We know
Force = G (m₁m₂/d²)
(a) F(net) = F₁ + F₂ + F₃
G (mm(p)/d²) + G (mm(p)/d²) + 2G (mm(p)/2d²)
|F(net)| = G[ mm(p) / d² ](√2 + 1)
= [6.67 x 10⁻¹¹ x 1 x (0.015) / (0.5)² ] (√2 + 1) = 9.7 x 10⁻¹² N
The magnitude of the force is 9.7 x 10⁻¹² N.
Direction 45° counter clockwise
(b) Initial velocity U(p) = √2Gm(2+√2/d - 2/150)
= √2 x 6.67 x 10⁻¹¹(2 + √2 / 0.5 - 2/150)
= 3 x 10⁻⁵ m/s
Therefore, the velocity at which it moves is 3 x 10⁻⁵ km/s.
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this wire has a 221 ma current moving to the right. ignoring any external fields, such as the earth, what is the magnetic force on a proton that is 5.8 millimeters from the wire and moving 5800 m/s?
The magnetic force on a proton that is 5.8 millimeters from the wire and moving 5800 m/s will be ( 7.15×10 ^−24)i^
Define magnetic field.
An electric charge, an electric current, and magnetic materials are all affected magnetically by a magnetic field, which is a vector field. A force perpendicular to the magnetic field and its own velocity acts on a moving charge in a magnetic field.
Assume the particle is at a distance d in the +y direction and the current is flowing in the +x direction (away from the wire). Afterward, the magnetic field at a proton's position with charge q is
B =(μ0 i/2πd) ^k
Thus,
F=qv × B
=qv ×(μ0 i/2πd) ^k
In this situation,
v =v(− j)
where v is the speed and is a positive value and q>0. Thus,
F =q(-j) ×(μ0 i/2πd) ^k
= − 4(π×10 ^−7 T.m/A)(0.221A)(1.60×10 ^−19)(5800m/s)i^/ {2π(5.8m)}
=( 7.15×10 ^−24)i^.
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Mass (kg) Weight (N) 0.05 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275 0.300 Displacement (Ay) 15 cm 23cm 30cm 40cm 48cm 55cm 63cm 71cm 80cm 90cm 97cm 1. Calculate the weight for each mass and fill in the middle column. Show the work for one of these calculations to receive credit. (5 points)
Here, we need to calculate weight.
Weight is given as the product of mass and gravity. This weight over here can also be denoted by force and it is said to be the force exerted by the bodies on the Earth.
If we take the gravity to be 10 m/s²,
then the weight for each given mass will be,
weight of 0.05 kg = 0.05*10 = 0.5 N
weight of 0.075 kg = 0.075 * 10 = 0.75 N
weight of 0.100 kg = 0.100 * 10 = 1 N
weight of 0.125 kg = 0.125 * 10 = 1.25 N
weight of 0.150 kg =0.150 * 10 = 1.5 N
weight of 0.175 kg = 0.175 * 10 = 1.75 N
weight of 0.200 kg = 0.200 * 10 = 2 N
weight of 0.225 kg = 0.225 * 10 = 2.25 N
weight of 0.250 kg = 0.250 * 10 = 2.5 N
weight of 0.275 kg = 0.275 * 10 = 2.75 N
weight of 0.300 kg = 0.300 * 10 = 3 N
Therefore, through this we got to know that the weight of the body is also the force exerted by the body on the Earth.
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an astronaut on mars (mass 6.42×1023kg , radius 3.39×106m ) launches a probe straight upward from the surface at 3.00×103m/s . what is the maximum height above the surface that the probe reaches? neglect air resistance and the gravitational pull of the two small moons of mars.
Answer:
H = 1 200 km
Explanation:
Given:
M = 6.42·10²³ kg
R = 3.39·10⁶ m
V₀ = 3.00·10³ m/s
______________
H - ?
Acceleration of free fall on Mars:
g = G·M / R²
g = 6.67·10⁻¹¹·6.42·10²³/ (3.39·10⁶)² ≈ 3.73 m/s²
The maximum height above the surface that the probe reaches:
H = V₀² / (2·g)
H = (3.00·10³)² / (2·3.73) ≈ 1 200 000 m = 1 200 km
A gas is taken through the cyclic process described in the figure. (The x axis is marked in increments of 2.5 m3.;) P (kPa) V (m3) (a) Find the net energy transferred to the system by heat during one complete cycle. (b) If the cycle is reversed-that is, the process follows the path ACBA-what is the net energy input per cycle by heat?
The correct solutions are -
(a) The net energy transferred to the system by heat during one complete cycle is 15 kJ
(b) The net energy input per cycle by heat is -15 kJ
The net energy transferred to the system is equal to work done. The work done will be calculated by the calculating the area enclosed in the figure.
The area = 1/2 × (8 - 2) × 5
Performing multiplication and division on Right Hand Side of the equation
Work done = 1/2 × 6 × 5
Work done = 3 × 5
Work done = 15 kJ
On reversing the cycle, the net energy input per cycle be heat will be -15kJ.
Hence, work done is 15 kj and net energy input is -15kJ.
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The complete question is attached in the figure.
if a diesel cycle and an otto cycle work at the same compression ratio, the ideal cycle with the lowest thermal efficiency is:
When a diesel cycle and Otto cycle work at the same compression ratio, the ideal cycle with the lowest thermal efficiency is Otto cycle because the area shown in the P-V graph for the same ratio is more than diesel cycle.
What is compression ratio?In an engine cylinder the ratio of maximum and minimum volume of the combustion chamber and cylinder is termed as compression ratio.
Hence, When a diesel cycle and Otto cycle work at the same compression ratio, the ideal cycle with the lowest thermal efficiency is Otto cycle because the area shown in the P-V graph for the same ratio is more than diesel cycle.
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when a particular metal is illuminated with photons, one electron is observed for each absorbed photon. what effect would decreasing the wavelength and number of photons have on the electrons leaving the surface?
The numbers of electrons leaving the surface would decrease if number of photons and wavelength will be decreased.
Since, number of electrons ejects out from the surface which is expose to photons attack is totally dependent on the amount of photons striking that open area in per unit time.
When count of photons would decrease, in that case count of those photons which have frequency greater than the threshold frequency will be lesser and due to that count of electrons will also decrease.
Similarly, photons which are able to eject the electrons from the surface have certain wavelength which is greater than threshold wavelength. In that case count of photons which are able to eject out the electrons will also decrease.
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an astronomer has calculated the radius of a black hole to be 51.0 au by observing its period of variability in brightness. what period, in hours, did she observe?
The astronomer will take 0.086 hours to observe the radius of the black hole.
A black hole is a place in space where gravity pulls so hard that even light cannot escape.
The astronomer has calculated the radius of a black hole to be 51.0 au by observing its period of variability in brightness.
'au' is the abbreviation for astronomical unit which is a unit of length used to measure the distance from Earth to sun.
1 au = 93 million kilometers
Also the radius is calculated on the variability in brightness, i.e. speed of light can be considered
Speed of light = 3 * [tex]10^{8}[/tex] m/s
So according to the formula of speed, time can be calculated as
time = distance / speed
time = 93 * [tex]10^{9}[/tex] / 3 * [tex]10^{8}[/tex]
time = 310 seconds
1 second = 0.0002 hour
310 seconds = 0.086 hour
The astronomer observed for 0.086 hours.
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explain the difference between the if then block and the if then else block: how does each work? how do we know which to use?
If you want to tell a block of code to run only if a certain condition is true, use the if statement. If the same condition is false, use else to declare that a different block of code should be run.
The most fundamental control flow expression is the if-then clause. It instructs your software to run a specific chunk of code only when a specific test returns true. For instance, the Bicycle class might only permit the brakes to slow the bicycle down after it is moving.
When a "if" clause evaluates to false, an alternative path of execution is provided by the if-then-else statement. If the brakes are applied while the bicycle is not moving, you might use an if-then-else clause in the apply Brakes method to do some action.
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what do asteroids and comets have in common? question 7 options: most are unchanged since their formation in the solar nebula. they have similar orbital radii. they have nothing in common with each other. they have a similar range of orbital inclinations.
The majority of comets and asteroids have not changed much since they were formed in the nebula.
What components make up comets?
The principal components of comets, which resemble dirty snowballs, are ice and freezing carbon dioxide, as well as some sand and biological molecules that were left over from Planetary System's origin. They function as "time capsules," revealing to us the circumstances of our Known Universe 4,5 billion years ago.
Which comet made the largest impact on Earth?
The nucleus of this comet has a diameter of 119 kilometers, according to recent measurements made the with Hubble Space Telescope. making it by far the largest comet ever discovered. Only 5 kilometers broad, the asteroid collision that triggered the last extinction event on Earth about 65 million years ago.
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a uniform block of granite in the shape of a book has face dimensions of 18 cm and 13 cm and a thickness of 1.2 cm. the density (mass per unit volume) of granite is 2.64 g/cm3. the block rotates around an axis that is perpendicular to its face and half way between its center and a corner. its angular momentum about that axis is 0.104 kg · m2/s. what is its rotational kinetic energy about that axis?
The rotational kinetic energy is 0.62 J.
How do you find rotational kinetic energy?The rotational kinetic energy, also known as "rotational mass," is the moment of inertia, or "rotational mass," of a rotating rigid body or system of particles, and is given by the formula K=12I2 K = 1 2 I 2.The definition of rotational energy, sometimes referred to as angular kinetic energy, is as follows: It is the portion of an object's total kinetic energy that results from rotation. The rotational inertia and the square of the angular velocity have a direct relationship with rotational kinetic energy.Moment of inertia, I = 8.04 times 1037 kg m2, and angular velocity, omega = 7.29 times 10-5 rad per second. As a result, the rotational kinetic energy is 2.13 x 1029 J.Step 1: Given Data
l = 20 cm = 0.2 m
w = 15 cm = 0.15 m
t = 1.2 cm = 0.012 m
ῤ = 2.64 g / [tex]cm^{3}[/tex] = 2.64 x [tex]10^{-3}[/tex] x [tex]10^{6}[/tex] kg / [tex]m^{3}[/tex]
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a point mass is rotation about a rotation axis you increase its distance from that axis by a factor of two by what factor does its moement ofd inertia about that axis increase
When we increase the distance by two, the moment of inertia increases by a factor of four.
A measure of an object's resistance to changes in its rotating motion, the moment of inertia (commonly abbreviated as "I") is used in physics. It measures the amount of mass disposed about a rotational axis. The equivalent of mass in linear motion is the moment of inertia in rotational motion.
The idea of a moment of inertia is essential to rotational dynamics and is applied in many branches of mechanics, engineering, and physics. It is essential for understanding how spinning things such as wheels, gears, flywheels, and heavenly bodies like planets move.
The moment of inertia is given by:
I = mr²
Here, mass (m) and distance (d).
If we increase the distance from r to 2r. The new moment of inertial is:
I = m(2r)²
I = 4mr²
Hence, when we increase the distance by two, the moment of inertia increases by a factor of four.
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a vehicle with will take longer to stop. a. worn brakes b. under-inflated tires c. worn tires d. all of the above
The vehicle with take longer to stop is worn brakes , under-inflated tires and worn tires
Which braking system do you usually use to slow down your vehicle while driving?Controlled braking is a hard braking technique that applies just the right amount of pressure to slow your car without throwing it off balance. This lets you keep both your front and back wheels effectively traction. With the cover brake technique, the change from accelerating to braking is smooth.
The master cylinder's hydraulic pressure squeezes the brake pads on either side of the rotor cylinder acting on a caliper, which is located slightly outside the rotor and holds the brake pads. Friction between the pads and the rotor causes the car to slow down and halt.
The secret to doing this is to apply normal braking until the vehicle slows to about walking speed, at which point you should lift the brake pedal slightly to reduce the force of the brakes.
The complete question is : What are four factors that affect breaking?
a vehicle with will take longer to stop. a. worn brakes b. under-inflated tires c. worn tires d. all of the above
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why can you assume that the Mechanical energy is equal to the Initial gravitational energy
The Mechanical energy is equal to the Initial gravitational energy as mechanical energy is stored in the object as gravitational potential energy.
What is law of conservation of energy?
Energy cannot be created or destroyed, according to the rule of conservation of energy. However, it is capable of change from one form to another.
An isolated system's total energy is constant regardless of the types of energy present. The law of energy conservation is adhered to by all energy forms. The law of conservation of energy essentially says that:
The total energy of the system is conserved in a closed system, also known as an isolated system.
Therefore, in a closed system like the universe, if energy is lost in one area, energy must be gained in a different area of the system by an equal amount. There is no known instance of the conservation of energy being broken, despite the fact that it cannot be proven.
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Please hurry
Part A: A force of 8 N is exerted on a box with a mass of 2 kg. What is the acceleration of the
box?
Part B:If the box accelerates from rest to a velocity of 4 m/s, what is the impulse?
hope this helps solve your question
A runner accelerates toward the finish line. Identify the action force in the example.
The runner's feet pressing against the ground serves as the example's action force.
Describe a force.A push or pull of an item or physical body may be described as a force. This change in motion, known as acceleration, often arises from the interaction of the object or physical body with another.
Newton's Second Law of Motion states that a physical body's acceleration and mass have a significant impact on the force acting on it.
An example of an action force in this situation is the pressure put on the ground by the runner's feet as they sprint faster toward the finish line.
The runner's feet pressing against the ground serves as the example's action force.
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what is the longest wavelength of light (in nm) for which all three metals will emit photoelectrons?
The 520 nm wavelength is the longest at which a metal will emit an electron.
The definitions of wavelength and frequencyThe wavelength, which is also the distance between two wave crests and troughs, is the measurement of wave length. In cycles per second (Hz), the term "frequency" refers to the number of vibrations that cross a specific area in a second (Hertz). This article talks about the relationship between wavelength and frequency.
The wavelength is what.The length of a waveform signal that is propagating in space or over a wire is measured by the separation between identical points (adjacent crests) in the adjacent cycles. This length is often stated in meters (m), centimeters (cm), or millimeters (mm) in wireless systems (mm).
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an automobile sounds its horn while passing an observer at 25.5 m/s. the actual horn frequency is 405 hz. assume the speed of sound is 345 m/s. find its frequency heard by the observer while the car is approaching.
The frequency heard by the observer while the car is approacing 437.3 Hz.
What is doppler effect?
A wave's frequency changes in response to an observer moving in respect to the wave source, which is known as the Doppler effect or Doppler shift. The change in pitch that happens as an automobile approaches and drives away from a spectator while sounding its horn is a common way to demonstrate doppler shift.
By using Doppler's Formula:
fo = v+vo/v+vs x fs
where,
fo = observer frequency of sound
v= speed of sound waves
vo= observer velocity
vs= source velocity
fs= actual frequency of sound waves
It is given that,
fs= 405Hz
vs= 25.5 m/s
v= 345 m/s
fo= 0 m/s
Observer to source = Positive
Source to observer = Negative
fo = v+vo/v+vs x fs
fo = 345/ 345 - 25.5× 405
fo = 437.3 Hz
Hence, The frequency heard by the observer is 437.3 Hz.
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The frequency heard by the observer while the car is approacing 437.3 Hz.
What is doppler effect?
A wave's frequency changes in response to an observer moving in respect to the wave source, which is known as the Doppler effect or Doppler shift. The change in pitch that happens as an automobile approaches and drives away from a spectator while sounding its horn is a common way to demonstrate doppler shift.
By using Doppler's Formula:
fo = v+vo/v+vs x fs
where,
fo = observer frequency of sound
v= speed of sound waves
vo= observer velocity
vs= source velocity
fs= actual frequency of sound waves
It is given that,
fs= 405Hz
vs= 25.5 m/s
v= 345 m/s
fo= 0 m/s
Observer to source = Positive
Source to observer = Negative
fo = v+vo/v+vs x fs
fo = 345/ 345 - 25.5× 405
fo = 437.3 Hz
Hence, The frequency heard by the observer is 437.3 Hz.
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35 grams of salt is dissolved in 500 grams of total solution. What is the percent by mass of salt?
The percentage by mass of the salt in the solution is 7%
How do I determine the percentage of the salt?Percentage composition can be obtained by using the following formula:
Percentage = (mass of solute / mass of solution) × 100
Now, we shall determine the percentage of the salt as illustrated below:
Mass of salt = 35 gramsMass of solution = 500 gramsPercentage of salt =?Percentage = (mass of solute / mass of solution) × 100
Percentage of salt = (35 grams / 500 grams) × 100
Percentage of salt = 7%
Thus, we can conclude that the percentage of the salt is 7%
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what minimum speed must the small sphere have in order to come within 5.00 cm of the surface of the large sphere?
The minimum speed must the small sphere have is v = 145.56 m/s
What is law of conservation of energy?
According to the rule of conservation of energy, energy cannot be generated or destroyed; it can only be transformed from one type of energy to another. This indicates that unless energy is added from outside, a system always has the same quantity of energy.
According to the given question,
Let the speed given to small charge q = v
Initially there is only Kinetic Energy present in the system , and potential energy is zero. The initial KE given to q is all transformed to Potential energy at distance r = 9.00 + 5.00 = 14.00 cm or 0.14 m from Q where q comes to rest due to the repelling forces.
Therefore, Using Energy Conservation -
PE = (qkQ)/r
KE = 1/2mv^2
PE = KE
1 / 2 * m * [tex]v^2[/tex] = Kq*Q/r
1 / 2 * 6 * [tex]10^-5[/tex] * [tex]v^2[/tex] = 8.9 * [tex]10^9[/tex] * 5 * [tex]10^-6[/tex] * 2* [tex]10^-6[/tex] / 0.14
v = [tex]\sqrt{(0.63571 * 10^5)/3)} m/s[/tex]
v = 145.56 m/s
Minimum speed must the small sphere have, v = 145.56 m/s
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Calculate the total mass of the protons and electrons in 19 9f. Use 1. 007825 amu as the mass of 11h (mass of a proton and an electron).
We can conclude that total mass of protons and electrons in is 9.07043 u.
What is Atomic mass ?
Atomic mass means the sum of total number of protons and neutrons present in an atom.
When an atom is neutral then number of protons equal the number of electrons.
Mass of a proton equals to 1.007276 u, mass of neutron equals to 1.008664 u.
For example, in a atom there are total 9 protons and number of neutrons is 19 - 9 = 10.
Since, it is a neutral atom so number of electrons will also be 9.
So, total mass will be calculated as follows.
Total mass = 9 (mass of electron + mass of proton)
= 9 (1.007825 u)
= 9.07043 u
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consider an electron for which n 4, 3, and m 3. calculate the numerical value of (a) the orbital angular momentum and (b) the z component of the orbital angular momentum.
The L operates on [tex]\psi_3^3[/tex] eigenvalue will be equal to [tex]\sqrt{12}.[/tex]
z component of angular momentum is operates on [tex]\psi_3^3[/tex] gives [tex]L_z=3[/tex]
As per the data given in the question,
Quantum numbers of Electron n=4, l=3, and m=3.
Here, we need to find
(a) orbital angular momentum L and
(b) z component of orbital angular momentum [tex]\left(L_z\right)[/tex].
(a)
If orbital angular momentum (L) operates on spherical harmonic wave function of electron it gives an eigenvalue.
Then, we can write it as:
[tex]L^2 \psi_l^m=l(l+1) \hbar^2 \psi_l^m \\\\L \psi_l^m=\sqrt{l(l+1)} \hbar \psi_l^m[/tex]
Where, l is orbital quantum number and [tex]\hbar[/tex] is the reduced plank's constant.
We have l=3 and m=3
So,
[tex]& L \psi_3^3=\sqrt{3(3+1)} \hbar \psi_3^3 \\& L \psi_3^3=\sqrt{3(4)} \hbar \psi_3^3 \\& L \psi_3^3=\sqrt{12} \hbar \psi_3^3 \\& L=\sqrt{12} \hbar[/tex]
Therefore, the L operates on [tex]\psi_3^3[/tex] eigenvalue will be equal to [tex]\sqrt{12}.[/tex]
(b)
If z component of orbital angular momentum is operates on [tex]\psi_1^m[/tex], it give eigenvalue as follows,
[tex]L_z \psi_l^m=m_z \hbar \psi_1^m[/tex]
Here, [tex]m_z[/tex] is the magnetic quantum number.
[tex]L_z \psi_3^3=3 \hbar \psi_3^3 \\L_z=3 \hbar[/tex]
Therefore, if z component of angular momentum is operates on [tex]\psi_3^3[/tex] gives [tex]L_z=3[/tex]
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The numerical value of the orbital angular momentum is 1.8265719672742281e-34 J s, and the numerical value of the z component of the orbital angular momentum is 1.5818577255e-34 J s
The orbital angular momentum of an electron is given by the formula:
L = √l(l + 1) (h/2π)
where l is the orbital quantum number.
In this case, l = 3, so the orbital angular momentum is:
L = √3(3 + 1) (h/2π) = √12 (h/2π) = 1.8265719672742281e-34 J s
The z component of the orbital angular momentum is given by the formula:
Lz = m(h/2π)
where m is the magnetic quantum number.
In this case, m = 3, so the z component of the orbital angular momentum is:
Lz = 3(h/2π) = 1.5818577255e-34 J s
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