Answers
The electron's distance from the nucleus in the 1s state of a hydrogen atom is A = [(r * (a^3 / 4√π) * ∫ e^(-2r/a) dr) - (a^3 / 4√π) * (∫ e^(-2r/a) dr)^2] from 0 to ∞ = [(r * (a^3 / 4√π) * (a/2)) - (a^3 / 4√π) * (a/2)^2].
To find the expectation value of the electron's distance from the nucleus in the 1s state of a hydrogen atom, we need to calculate the quantity Ar, where A is given by:
A = ⟨r⟩ = ∫ r * ψ(1s) * r^2 dr from 0 to ∞
First, let's express ψ(1s) in terms of the radial wavefunction R(r):
ψ(1s) = R(r) * Y(0,0) [Since the 1s state has azimuthal quantum number l = 0 and magnetic quantum number m = 0]
The radial wavefunction R(r) for the 1s state is given by:
R(r) = (1 / √π * a^(3/2)) * e^(-r/a)
Now, let's calculate A:
A = ∫ r * ψ(1s) * r^2 dr from 0 to ∞
= ∫ r * (1 / √π * a^(3/2)) * e^(-r/a) * r^2 dr from 0 to ∞
We can use integration by parts to simplify this integral. Let's define u = r and dv = (1 / √π * a^(3/2)) * e^(-r/a) * r^2 dr.
Taking the differentials, we have du = dr and v = ∫ (1 / √π * a^(3/2)) * e^(-r/a) * r^2 dr.
Integrating v, we can use the given integrals:
v = ∫ (1 / √π * a^(3/2)) * e^(-r/a) * r^2 dr
= (a^3 / 4√π) * ∫ e^(-2r/a) dr [Using the given integral]
Now, applying integration by parts:
∫ u dv = uv - ∫ v du
∫ r * (1 / √π * a^(3/2)) * e^(-r/a) * r^2 dr
= (r * v) - ∫ v du
= (r * (a^3 / 4√π) * ∫ e^(-2r/a) dr) - ∫ [(a^3 / 4√π) * ∫ e^(-2r/a) dr] dr
Simplifying the expression:
A = [(r * (a^3 / 4√π) * ∫ e^(-2r/a) dr) - (a^3 / 4√π) * ∫ ∫ e^(-2r/a) dr dr] from 0 to ∞
The integral ∫ ∫ e^(-2r/a) dr dr can be expressed in terms of the given integrals:
∫ ∫ e^(-2r/a) dr dr = (∫ e^(-2r/a) dr)^2
= (a/2)^2 [Using the given integral]
Now, substituting the values and evaluating the limits:
A = [(r * (a^3 / 4√π) * ∫ e^(-2r/a) dr) - (a^3 / 4√π) * (∫ e^(-2r/a) dr)^2] from 0 to ∞
= [(r * (a^3 / 4√π) * (a/2)) - (a^3 / 4√π) * (a/2)^2]
For more such questions on nucleus,click on
https://brainly.com/question/12602839
#SPJ8
Related Questions
A 64.0 cm long cord is vibrating in such a manner that it forms a standing wave with two antinodes. (The cord is fixed at both ends.) Which harmonic does this wave represent
Answers
Answer:
the wave represents the second harmonic.
Explanation:
Given;
length of the cord, L = 64 cm
The first harmonic of a cord fixed at both ends is given as;
[tex]f_o = \frac{V}{2L}[/tex]
The wavelength of a standing wave with two antinodes is calculated as follows;
L = N---> A -----> N + N ----> A -----> N
Where;
N is node
A is antinode
L = N---> A -----> N + N ----> A -----> N = λ/2 + λ/2
L = λ
The harmonic is calculated as;
[tex]f = \frac{V}{\lambda} \\\\f = \frac{V}{L} = 2(\frac{V}{2L} ) = 2(f_o) = 2^{nd} \ harmonic[/tex]
Therefore, the wave represents the second harmonic.
L = λ
The kinetic energy and the potential energy of the cannonball is constantly ________ as it travels through the air.
A. Changing
B. Increasing
C. Constant
D. Decreasing
Answers
Answer:
C. Constant
Explanation:
The total energy of the cannonball remains constant as it travels through the air.
Answer:
Explanation:
hi my name is Ava
The potential energy of a mass-spring system when the spring is fully compressed and the mass is at rest is 200 J. After releasing the mass, assuming there is no dissipative force, the system will oscillate. At a point during the oscillation the potential energy of the system is 50 J. What is the kinetic energy of the mass at that point
Answers
Answer:
150 J
Explanation:
If there is not any dissipative force in the system, the mass and the spring will oscillate eternally., but of course, we assume this is a theoretical situation. The conservation of energy in a system implies that the sum of the potential energy plus kinetic energy remains constant, therefore if in the initial point the mass has 200 J (potential energy) and is at rest ( kinetic energy = 0) the overall energy at the beginning is 200 J. At any point of the oscillation if the potential energy is 50 J the kinetic energy must be 150 J.
Scientists have concluded that the uppermost part of the mantle is partially-molten. Which observation helped them reach this conclusion?
Answers
Answer:
P and S waves slow down when they reach this layer. The asthenosphere, also known as the magma chamber, is the uppermost component of the mantle. This layer is partially molten and is a ductile zone in a tectonically poor state.
It's almost hard and seismic waves move through the asthenosphere at a slow rate. The fragile lithosphere and the uppermost portion of the asthenosphere are assumed to be rigid.
seismic waves travel more quickly through denser materials and therefore generally travel more quickly with the depth it moves more slowly through a liquid than a solid. Molten areas within the Earth slow down P waves and stop S waves because their shearing motion cannot be transmitted through a liquid. Partially molten areas may slow down the P waves and attenuate or weaken S waves.
hope this helps...
S and P wave slow down and stop in the uppermost part of the mantle. - For this, scientists have concluded that the uppermost part of the mantle is partially-molten.
What is mantle?A planetary body's mantle is a layer that is surrounded by the crust on top and the core underneath. The largest and most substantial layer of a planetary body, mantles are often comprised of rock or ice. Planetary bodies that have undergone density differentiation typically have mantles. Mantles are found on all terrestrial planets (including Earth), many asteroids, and a few planetary moons.
Between the crust and the outer core, there is a silicate rock layer known as the Earth's mantle. Despite being mostly solid, it behaves like a viscous fluid over geological time. Oceanic crust is created by the partial melting of the mantle at mid-ocean ridges, and continental crust is created by the partial melting of the mantle at subduction zones.
Learn more about mantle here:
https://brainly.com/question/28827790
#SPJ2
a)
What is the net force on the refrigerator shown to the right?
200 N
1,000 N
50 N
= Fg
1,000 N = F.
b) Calculate the mass of the refrigerator.
c) What is the refrigerator's acceleration?
Answers
Answer:
50N
Explanation:
is the opposing fotce
A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to 2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 7 ft/s. (Use g
Answers
Correct question is;
A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to √2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 7 ft/s. (Use g = 32 ft/s²)
Answer:
x(t) = 7te^(-2t√2)
Explanation:
We are given;
Weight; W = 8 lbs
mass; m = W/g
g = 32 ft/s²
Thus;
m = 8/32
m = ¼ slugs
From Newton's second law we can write the equation as;
m(d²x/dt²) = -kx - β(dx/dt)
Rearranging this, we have;
(d²x/dt²) + (β/m)(dx/dt) + (k/m)x = 0
Where;
β is damping constant = √2
k is spring constant = W/s
Where s = 8ft - 4ft = 4ft
k = 8/4
k = 2
Thus,we now have;
(d²x/dt²) + (√2/(¼))(dx/dt) + (2/(¼))x = 0
>> (d²x/dt²) + (4√2)dx/dt + 8x = 0
The auxiliary equation of this is;
m² + (4√2)m + 8 = 0
Using quadratic formula, we have;
m1 = m2 = -2√2
The general solution will be gotten from;
x_t = c1•e^(mt) + c2•t•e^(mt)
Plugging in the relevant values gives;
x_t = c1•e^(mt) + c2•t•e^(mt)
At initial condition of t = 0, x_t = 0 and thus; c1 = 0
Also at initial condition of t = 0, x'(0) = 7 and thus;
Since c1 = 0, then c2 = 7
Thus,equation of motion is;
x(t) = 7te^(-2t√2)
Raven knows that ammonia will react with vinegar when they are both dissolved in water. She's concerned the reaction will go too quickly. How can she slow down the reaction?
Question 13 options:
Increase the concentration of dissolved substances
Decrease the concentration of dissolved substances
Add a catalyst
There's nothing she can do to change the rate of reaction.
Question 14 (2 points)
Which of the following is a solution?
Question 14 options:
Popcorn
A salad
Pure water
Salt dissolved in water
Question 15 (2 points)
The picture shows two solutions of salt water. Which solution is more concentrated (has a higher concentration)?
Question 15 options:
The first solution is more concentrated
The second solution is more concentrated
The solutions have the same concentration.
Question 16 (2 points)
What must occur for particles to react?
Question 16 options:
They must collide
They must photosynthesize
They must condense
They must melt
Question 17 (3 points)
In your opinion, what the most important OR interesting thing from this unit? If you didn't find anything interesting, please write one thing that you learned.
Write a full sentence, please.
Question 17 options:
Answers
A solution is a homogeneous mixture, which may be liquid, gas or solid, formed by dissolving one or more substances.
According to this question, a salt dissolved in water is an example of solution because it involves a solute and a solvent.
The rate of a chemical reaction can be decreased by reducing the concentration of the reactants so as not to provoke a reaction.
In a chemical reaction, the particles of the reactants must collide to initiate the reaction.
Learn more about solution at: https://brainly.com/question/1616939
#SPJ1
Need a 5 paragraph essay in the eartsh layers and how they function/ benefit the earth!
Answers
There is more to the Earth than what we can see on the surface. In fact, if you were able to hold the Earth in your hand and slice it in half, you'd see that it has multiple layers. But of course, the interior of our world continues to hold some mysteries for us. Even as we intrepidly explore other worlds and deploy satellites into orbit, the inner recesses of our planet remains off limit from us.
However, advances in seismology have allowed us to learn a great deal about the Earth and the many layers that make it up. Each layer has its own properties, composition, and characteristics that affects many of the key processes of our planet. They are, in order from the exterior to the interior – the crust, the mantle, the outer core, and the inner core. Let's take a look at them and see what they have going on.
Like all terrestrial planets, the Earth's interior is differentiated. This means that its internal structure consists of layers, arranged like the skin of an onion. Peel back one, and you find another, distinguished from the last by its chemical and geological properties, as well as vast differences in temperature and pressure.
Explanation:
Select the correct answer.
F₁ = 70 N
F₂ = 15 N
8
F₁
W = 80 N
Use this free body diagram to help you find the magnitude of the force F₁ needed to keep this block in static equilibrium.
Answers
Explanation:
F1 will have to have 65 N vertical up force to balance the net 65 N down on the body AND it will have to have 70 N horizontal to the right to balance the 70 N force that is acting to the left
Magnitude = sqrt ( 65^2 + 70^2) = 95.5 N
What are the five classes of objects that orbit the sun?
Answers
Electricity is distributed from electrical substations to neighborhoods at 13000 V. This is a 60 Hz oscillating (AC) voltage. Neighborhood transformers, seen on utility poles, step this voltage down to the 120 V that is delivered to your house.
A. How many turns does the primary coil on the transformer have if the secondary coil has 120 turns?
Answers
Answer:
the number of turns in the primary coil is 13000
Explanation:
Given the data in the question;
V₁ = 13000 V
V₂ = 120 V
N₁ = ?
N₂ = 120 turns
the relation between the voltages and the number of turns in the primary and secondary coils can be expressed as;
V₁/V₂ = N₁/N₂
V₁N₂ = V₂N₁
N₁ = V₁N₂ / V₂
so we substitute
N₁ = (13000 V × 120 turns) / 120 V
N₁ = 1560000 V-turns / 120 V
N₁ = 13000 turns
Therefore, the number of turns in the primary coil is 13000
A man walks 30 m to the west, then 5 m to the east in 45 seconds.
What is his average speed?
Answers
What voltage would be measured across the 15 ohm resistor?
A)
2.5 volts
B)
5.0 volts
C)
7.5 volts
D)
10 volts
Answers
Answer:
7.5 volts
Explanation:
I did it on USA Testprep
Samir is waiting for a slow reaction to finish. What is the best way to make the reaction go faster?
Question 12 options:
Put it in the fridge where it is cold
Cover it with a blanket so it's dark
Warm it up on the stove
There is nothing you can do to change the speed of the reaction
Answers
In general, option c - warming it up on the stove - is often an effective method to increase the reaction rate.
Increasing the temperature of a reaction generally leads to faster reaction rates. This is because higher temperatures provide more thermal energy to the reactant particles, causing them to move faster and collide more frequently. The increased collision frequency and energy lead to more successful collisions and a higher likelihood of effective molecular interactions, which speeds up the reaction. On the other hand, options a and b - putting it in the fridge where it is cold or covering it with a blanket to make it dark - are unlikely to have a significant effect on the reaction rate. While temperature can influence reaction rates, cooling the reaction or making it dark typically reduces the kinetic energy of the particles, resulting in slower reaction rates. Option d - there is nothing you can do to change the speed of the reaction - is not accurate. The reaction rate can be influenced by various factors such as temperature, concentration, catalysts, and surface area, among others. By manipulating these factors, it is often possible to control and change the speed of a reaction. Hence option c, is correct
for more questions on reaction
https://brainly.com/question/4431224
#SPJ8
3) Which of the following can affect the success of a start-up business?
A) the entrepreneur's ability to communicate
B) the entrepreneur's ability to resolve conflict
C) the entrepreneur's ability to work with his employees
D) all of the above
Answers
Answer:
all of the above.
Explanation:
all of these qualities are crucial in order to have a successful business.
What is the approximate surface temperature of the 'White Dwarfs'?.
2,500-5,000 K
5,000-10,000
10,000-15,000 K
15,000 K-35,000 K
Answers
Answer:
5,000-10,000 K
Explanation:
make me your brainlist pls
A car accelerates from rest to 35m/s in a distance of 88 m. What was its acceleration in m/s2, assumed constant?
Answers
Answer:
6.96ms/2 or 7ms/2
Explanation:
v2=u2 +2as second equation of motion
u=o
v=35
S=88
a=?
35^2=0^2 +2xax88
=1225 =0+176a
1225=176a
1224/176=6.96ms/2 or 7ms/2
This photo shows a beam of light entering and exiting a piece of glass.
What happens when the light enters the glass?
A. The light is absorbed.
B. The light is reflected.
C. The light is scattered.
D. The light is refracted.
Answers
Answer:
D. The Light Is Refracted
Explanation:
<3
A loop of wire carrying a current of 2.0 A is in the shape of a right triangle with two equal sides, each 15 cm long. A 0.7 T uniform magnetic field is parallel to the hypotenuse. The total magnetic force on the two equal sides has a magnitude of:Group of answer choices0.30 N0 N0.51 N0.41 N
Answers
Answer:
the total magnetic force on the 2 sides of the wire is 0.30 N
Option a) 0.30 N is the correct answer
Explanation:
Given the data in the question;
both the sides of the right angled triangle is the same and the magnetic is in the plane of the triangle and is perpendicular to the hypotenuse.
hence, angle between the magnetic field and both the sides of the triangle is 45 degrees.
∅ = 45°
I = 2.0 A
L = 15 cm = 0.15 m
B = 0.7 T
Total magnetic force on the 2 sides of the wire will be;
F = 2BILsin∅
we substitute
F = 2 × 0.7 × 2.0 × 0.15 × sin(45°)
F = 0.42 × 0.70710678
F = 0.2970 ≈ 0.30 N
Therefore, the total magnetic force on the 2 sides of the wire is 0.30 N
Option a) 0.30 N is the correct answer
In the past, asteroids striking the earth have produced disastrous results. If we discovered an asteroid on a collision course with the earth, we could, in principle, deflect it and avoid an impact by focusing a laser on the surface. Intense surface heating from the laser could cause surface material to be ejected into space at high speed.
Required:
How would this deflect the asteroid?
Answers
Answer:
Explained below.
Explanation:
We are told that the surface material is ejected into space at a high speed. This means that it will have a likely high momentum as well.
Now, we can say that the total momentum is conserved because the entire asteroid system behaves like an isolated system.
Also, as the surface material is moving with the high momentum like we established earlier, it will cause the asteroid to move with a speed in an opposite direction which also means deflection in an opposite direction.
Answer:
Explained below.
Explanation:
The material ejected from the surface of the asteroid would have a significant momentum. Since the asteroid and all its material is an isolated system, the ejection would cause an oppositely directed change in momentum of the asteroid, according to the law of conservation of momentum.
The ejected material is analogous to gases expelled from a rocket, and the asteroid is analogous to a rocket.
Please help me with this question. Every help is appreciated.
Answers
Answer:
Change in KE = +1.96×10^4 J while the change in ME = 0 J
What is respiration?
Answers
Answer:
taking in oxygen and giving out carbon dioxide is called respiration
Answer:
i think that respiratiln is when you breqth
How many gallons of water does it take to produce the following:
a. Cheeseburger
b. Pound of butter
c. A pair of jeans
Answers
Answer:
a. 660 gallons
b.665 gallons
c. 1,800
You are testing a new amusement park roller coaster with an empty car with a mass of 130 kg . One part of the track is a vertical loop with a radius of 12.0 m . At the bottom of the loop (point A) the car has a speed of 25.0 m/s and at the top of the loop (point B) it has speed of 8.00 m/s . Part A As the car rolls from point A to point B, how much work is done by friction
Answers
Answer:
work done by friction = 5889 J
Explanation:
We are given;
Mass of car; m = 130 kg
Speed at point A; v1 = 25 m/s
Speed at point B: v2 = 8 m/s
Since radius is 12 m
At point A, distance is; y1 = 12 m
At point B, distance is; y2 = -12 m
Now, formula for work done by all the forces is given by the equation;
Total work;
W_gravity + W_others = K2 - K1
Where W_others is work done by other forces which is equal to work done by friction
Where K2 - K1 is change in kinetic energy.
W_grav is also change in potential energy and is expressed as;
W_grav = mgy1 - mgy2
K2 - K1 = ½m(v1)² - ½m(v2)²
Thus;
mgy1 - mgy2 + W_others = ½m(v1)² - ½m(v2)²
Making W_others the subject;
W_others = ½m(v1)² - ½m(v2)² + mgy2 - mgy1
Plugging in the relevant values;
W_others = (½ × 130 × 25²) - (½ × 130 × 8²) + (130 × 9.8 × -12) - (130 × 9.8 × 12)
W_others = 5889 J
Recall that I earlier said W_others = work done by friction.
Thus, work done by friction = 5889 J
20. How does a paraxylene crystallizer operate?
Answers
In the CrystPX Technology process, suspension crystallization of paraxylene (PX) in the xylene isomer mixture is used to produce paraxylene crystals. At the back end of the process, high paraxylene recovery is obtained by operating the crystallizers at colder temperatures.
Paraxylene crystals are created using the CrystPX Technology by suspending paraxylene (PX) in a mixture of xylene isomers. High paraxylene recovery is achieved at the end of the process by running the crystallizers at lower temperatures.
What does a paraxylene crystallizer operate?The paraxylene technology from BP, a novel method using single stage crystallization for paraxylene (pX) recovery, is licensed exclusively to Lummus Technology for use around the world.
This cutting-edge architecture makes the Lummus Technology/BP pX crystallization technology the most energy-efficient paraxylene recovery process, together with excellent feed impurity tolerance and low total unit fuel consumption.
The Lummus Technology/BP paraxylene process has a high degree of dependability, is inexpensive, and can take a variety of feed compositions.
Therefore, With the aid of isomerization over a non-noble metal catalyst, the yield of xylene is improved even further. Optimized fractionation lowers reboiler duty, resulting in less energy use and emissions.
Learn more about crystallizer here:
https://brainly.com/question/20725934
#SPJ2
FIRST CORRECT ANSWER GETS BRAINLIEST!!!
Answers
Answer:
Light is being absorbed
Hope this helps!
Light is being absorbed
Water can form large dewdrops in nature how would droplets made of isopropyl alcohol instead of water be different
Answers
Answer:
isopropyl alcohol would form smaller droplets, because it has lower surface tension than water has
Explanation:
Ap3x
The droplets made of isopropyl alcohol instead of water be smaller due to surface tension.
What is droplets?The single drop of a liquid in the form of sphere is called droplet.
Water can form large dewdrops in nature. Isopropyl alcohol would form smaller droplets, because it has lower surface tension than water.
Surface tension is the property of the liquid to acquire minimum surface area.
Thus, droplets made of isopropyl alcohol instead of water be smaller.
Learn more about droplet.
https://brainly.com/question/2926487
#SPJ2
Why do herbivores of the Serengeti migrate year after year
Answers
Answer:
The main reason is that very young calves are more noticeable to predators when mixed with older calves from the previous year
Explanation:
They are forced to migrate by carnivores that hunt them.
if matter cannot be created nor destroyed where did the matter in the univerce com from ???????
BIG BRAIN
Answers
i have no idea
I don't even know how we are here
When jeremiah stands in a swimming pool and looks at hid feet, his legs appear to be bent. Which is the term for this phenomenon?
A. Diffraction
B. Dispersion
C. Reflection
D. Refraction
Answers
Explanation: Refraction occurs when a medium bends the light rays of an object. Like water for instance as an example of a medium.