I hope this will help you. Here is the link http://web.physics.ucsb.edu/~phys6c/summer2006/hw4solutions
Red light of wavelength 630 nm passes through two slits and then onto a screen that is 1.3 m from the slits. The center of the 3rd order bright band on the screen is separated from the central maximum by 0.90 cm. a) What is the frequency of the light, the slit separation, and the angle of the 3rd order bright band
Answer:
a) f = 4.76 10¹⁴ Hz, b) d = 2.73 10⁻⁴ m, c) θ = 6.923 10⁻³ rad
Explanation:
a) In this problem the frequency of light is asked, let's use the relationship between the speed of the wave, its wavelength and its frequency
c = λ f
f = c /λ
f = [tex]\frac{3 \ 10^8}{630 \ 10^{-9}}[/tex]
f = 4.76 10¹⁴ Hz
b) slit separation (d)
the expression for the constructive interference of the double-slit experiment is
d sin θ = m λ
let's use trigonometry
tan θ = y / L
tan θ = [tex]\frac{sin \theta}{cos \theta}[/tex]
in general the angles are small, so we can approximate
tan θ = sin θ
tan θ = y/L
we substitute
d y / L = m λ
d = m L λ / y
we calculate
d = 3 1.3 630 10⁻⁹ /0.90 10⁻²
d = 2.73 10⁻⁴ m
c) the angle
tan θ = y / L
θ = tan⁻¹ y / L
θ = tan⁻¹ 0.9 10⁻² / 1.3
θ = tan⁻¹ 6,923 10⁻³
let's find the angle in radians
θ = 6.923 10⁻³ rad
An electron is confined in the 1s state of Hydrogen atom. Find ∆. Given that
∆ = ( in pic )
Help me pls!
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]
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a highway curve of radius 100 m, banked at an angle of 45 degrees, may be negotiated without friction at a speed of:
A car making this turn is pulled downward by its own weight, and pushed up by the road at an angle of 45°, so by Newton's second law,
• the net horizontal force on the car is
∑ F = N cos(45°) = m a = m v ² / R
• the net vertical force on the car is
∑ F = N sin(45°) - m g = 0
where
• N = magnitude of the normal force
• m = mass of the car
• a = v ² / R = centripetal acceleration of the car
• v = tangential speed of the car
• R = 100 m = radius of curvature
• g = 9.8 m/s² = acceleration due to gravity
From the net vertical force equation, we get
N = m g / sin(45°)
and substituting this into the net horizontal force equation and solving for v gives
(m g / sin(45°)) cos(45°) = m v ² / R
v = √(R g cos(45°) / sin(45°)) ≈ 31 m/s
We have that A highway curve of radius 100 m, banked at an angle of 45 degrees, may be negotiated without friction at a speed of
V=32m/s
From the question we are told
a highway curve of radius 100 m, banked at an angle of 45 degrees, may be negotiated without friction at a speed of:
Generally the equation for the Velocity is mathematically given as
[tex]V=\sqrt{rgtan\theta}[/tex]
Therefore
[tex]V=\sqrt{rgtan\theta}\\\\V=\sqrt{100*9.8*tan45}\\\\V=32m/s[/tex]
Therefore
A highway curve of radius 100 m, banked at an angle of 45 degrees, may be negotiated without friction at a speed of
V=32m/s
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What is the reason that the moon looks dimmer before eclipse? Why does it take some time to be brighter again after eclipse?
Answer:
Why does it take sometimes to be brighter again after eclipse? The moon looks dimmer before lunar eclipse because the moon enters into shadow of penumbra region of earth. As a result, the brightness of moon decreases and looks dimmer.
Explanation:
Answer: The moon looks dimmer before lunar eclipse because the moon enters into shadow of penumbra region of earth. As a result, the brightness of moon decreases and looks dimmer.
Explanation:
A rifle can shoot a 4.00 g bullet at a speed of 998 m/s. Find the kinetic energy of the bullet. What work is done on the bullet if it starts from rest?
Answer:
1992.008J
Explanation:
Two protons move with uniform circular motion in the presence of uniform magnetic fields. Proton one moves twice as fast as proton two. The magnitude of the magnetic field in which proton one is immersed is twice the magnitude of the magnetic field in which proton two is immersed. The radius of the circle around which proton one moves is r. What is the radius of the circle around which proton two moves
Answer:
r₂ = 4 r
Explanation:
For this exercise let's use Newton's second law with the magnetic force
F = q v x B
bold letters indicate vectors, the magnitude of this expression is
F = q v B sin θ
in this case we assume that the angle is 90º between the speed and the magnetic field.
If we use the rule of the right hand with the positive charge, the thumb in the direction of the speed, the fingers extended in the direction of the magnetic field, the palm points in the direction of the force, which is towards the center of the circle, therefore the force is radial and the acceleration is centripetal
a = v² / r
let's use Newton's second law
F = ma
q v B = m v² / r
r = [tex]\frac{qB}{mv}[/tex]
Let's apply this expression to our case.
Proton 1
r = \frac{qB_1}{mv_1}
Proton 2
r₂ = [tex]\frac{q \ B_2}{m \ v_2}[/tex]
in the exercise indicate some relationships between the two protons
* v₁ = 2 v₂
v₂ = v₁ / 2
* B₂ = 2B₁
we substitute
r₂ = [tex]\frac{q \ 2B_1}{m \ \frac{v_1}{2} }[/tex]
r₂ = 4 [tex]\frac{qB_1}{mv_1}[/tex]
r₂ = 4 r
When a car makes a sharp left turn, what causes the passengers to move toward the right side of the car? *
A centrifugal force
B inertia
C centripetal acceleration
D centripetal force
B, the body at rest becomes reluctant to start moving or a body in motion becomes
reluctant and stop moving once in motion in a straight line
an elevator of mass 250kg is carrying two persons whose masses are 50kg and 100kg. if the forces exerted by the motor is 3000N. calculate the mass of the bodies in the elevator.... Taking g as 10m/s²
Explanation:
mass=force*acceleration
mass=3000*10
mass=30,000
The mass of the bodies in the elevator is 400 kg.
The acceleration of the elevator is 2.5 m/s².
What is acceleration?Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of acceleration is meter/second² (m/s²).
Given parameters:
Mass of the elevator: M = 250 kg.
Mass of two persons: m₁ = 50 kg and m₂ = 100 kg.
Force exerted by the motor: F = 3000N.
g = 10 m/s².
Let, the acceleration of the elevator = a.
the mass of the bodies in the elevator :m= 250 kg. + 50 kg +100 kg. = 400 kg.
Now, F = mg - ma
⇒ 3000 = 400×10 - 400a
⇒ a = 1000/400 = 2.5 m/s²
Hence, the acceleration of the elevator is 2.5 m/s².
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An electron is travelling in the positive x direction. A uniform electric field is in the negative y direction. If a uniform magnetic field with the appropriate magnitude and direction also exists in the region, the total force on the electron will be zero. The appropriate direction for the magnetic field is:Group of answer choicesthe negative y directioninto the pageout of the pagethe negative x directionthe positive y direction
Answer:
into the page
Explanation:
Since the uniform electric field is in the negative y direction so its is -E and the electron is travelling in the positive x direction, it experiences an electric force F = -e × -E = + eE, so the electric force is in the positive y direction. Now since the net force on the electron is zero in the region of the magnetic field, it follows that the direction of the magnetic force is opposite to that of the electric force. Since the electric force is in the positive y direction, the magnetic force is in the negative y direction.
By the right hand rule, since the magnetic force is in the negative y direction and the electron moves in the positive x direction, it follows that the magnetic field is in the positive z direction, into the page.
What is the definition of the half-life of a radioactive isotope?
answer: The time it takes for half the parent nuclei in a sample to become daughter nuclei.
Answer: The half-life is the amount of time it takes for a given isotope to lose half of its radioactivity. If a radioisotope has a half-life of 14 days, half of its atoms will have decayed within 14 days. In 14 more days, half of that remaining half will decay, and so on.
IS
When a 0.622 kg basketball hits
the floor, its velocity changes from
4.23 m/s down to 3.85 m/s up.
What impulse was given to the
ball?
(Unit = kg*m/s)
Remember: up is +, down is -
Enter
Answer:
5.03
Explanation:
trust me
What happens to a light wave that is absorbed by matter
Answer:
In absorption, the frequency of the incoming light wave is at or near the energy levels of the electrons in the matter. The electrons will absorb the energy of the light wave and change their energy state.
Explanation:
Explain why it is not advisable to be in a garage when the car engine is being
heated.
Answer:
You can breathe in too much carbon monoxide, which will eliminate the flow of oxygen to your bloodstream and can kill you.
Explanation:
What is known as the amount of mass in
a given volume?
A. density
B. pressure
C. surface tension
D. mass pressure
A go-cart is traveling at a rate of 25 m/sec for 20 seconds. How far will the go cart travel?
Answer:
Distance travel by go-cart = 500 meter
Explanation:
Given:
Speed of go cart = 25 m/s
Time travel = 20 seconds
Find:
Distance travel by go-cart
Computation:
Distance = Speed x time
Distance travel by go-cart = Speed of go cart x Time travel
Distance travel by go-cart = 25 x 20
Distance travel by go-cart = 500 meter
Only one setup below will light the bulb. Which setup will light the bulb?
Answer:
A. it's got everything set.... correct connection
The setup that will light the bulb in the given different circuit diagram is circuit A, because it is the only circuit is that is closed.
What is a closed circuit?A complete circuit or closed circuit is the circuit that will allow the flow of electric current through it.
When a circuit is closed or complete, the connection of the different components of the circuit is complete.
From the image given, only option A has complete connection of different components of the circuit.
Thus, the setup that will light the bulb in the given different circuit diagram is circuit A, because it is the only circuit is that is closed.
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The angle between reflected ray and the normal line is
1. Angle of incident
2. Angle of reflection
3. Angle of refraction
Answer:
Angle(Δ) of ReflectionWhat is the term used to describe the
force pushing on an area or surface?
A. density
B. pressure
C. surface tension
D. volume
You are testing a new car using crash test dummies. Consider two ways to slow the car from 90 km/h (56 mi/h) to a complete stop:
i) You let the car slam into a wall, bringing it to a sudden stop.
ii) You let the car plow into a giant tub of gelatin so that it comes to a gradual halt.
In which case is there a greater impulse of the net force on the car?
(Prove and select below.)
a) in case (i).
b) in case (ii).
c) The impulse is the same in both cases.
d) The impulse of the first case > the impulse of the second case.
e) The impulse of the first case < the impulse of the second case.
Answer:
c) The impulse is the same in both cases.
Explanation:
What drives the car is the amount of movement of the car during its journey. In this case, we can consider that in the car, presented in the question above, the movement is generated through speed and friction on the track, the impact that makes the car stop, is not part of the movement and therefore, not part of the impulse. In the two situations presented, the speed of the car is the same, the same car and the same track were also used, which shows us that the impulse, in both situations, is the same.
A +3.4 x 10-6 C test charge experiences forces from two other nearby charges: a 3 N force due east and a 15 N force due west. What are the magnitude and direction of the electric field st the location of the test charge?
Answer:
3.53×10⁶ N/c due west
Explanation:
From the question
E = F'/q........................ Equation 1
Where E = Electric Field, F = Net Force, q = Charge.
But,
F' = F₂-F₁...................... Equation 2
Substitute equation 2 into equation 1
E = (F₂-F₁)/q................ Equation 3
Given: F₁ = 3 N due east, F₂ = 15 N due west, q = 3.4×10⁻⁶ C
Substitute these values into equation 1
E = (15-3)/(3.4×10⁻⁶)
E = 12/(3.4×10⁻⁶)
E = 3.53×10⁶ N/c due west
PLEASE HELP
the graph shows a plot of an objects velocity versus time for 15 seconds. is the acceleration of the object constant or changing? how do you know? what does this tell you about the net force on the object?
Answer:
It cannot be constant because if it does not change and each time it increases its strength and speed.
Explanation:
a Ferris wheel with a diameter of 35 m starts from rest and achieves its maximum operational tangential speed of 2.3 m/s in a time of 15 s. what is the magnitude of the wheels angular acceleration?
b. what is the magnitude of the tangential acceleration after the maximum operational speed is reached?
(a) The magnitude of the wheels angular acceleration is 0.0088 rad/s².
(b) The magnitude of the tangential acceleration after the maximum operational speed is reached is 0.153 m/s².
Angular acceleration of the wheel
The angular acceleration of the wheel is calculated as follows;
α = ω/t
ω = v/r
α = v/(rt)
α = (2.3)/(17.5 x 15)
α = 0.0088 rad/s²
Tangential acceleration of the wheela = v/t
a = (2.3)/15
a = 0.153 m/s²
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Credit-Card Magnetic Strips Experiments carried out on the television show Mythbusters determined that a magnetic field of 1000 gauss is needed to corrupt the information on a credit card's magnetic strip. (They also busted the myth that a credit card can be demagnetized by an electric eel or an eelskin wallet.) Suppose a long, straight wire carries a current of 7.0A . How close can a credit card be held to this wire without damaging its magnetic strip?
Answer:
14 μm
Explanation:
The magnetic field due to a long straight wire is B = μ₀i/2πr where μ₀ = permeability of free space = 4π × 10⁻⁷ H/m, i = current = 7.0 A and r = distance of credit card from magnetic field.
So r = μ₀i/2πB since B = 1000 gauss = 1000 G × 1 T/10000 G = 0.1 T
r = 4π × 10⁻⁷ H/m × 7.0 A/(2π × 0.1 T)
r = 2 × 10⁻⁷ H/m × 7.0 A/0.1 T
r = 14 × 10⁻⁷ H/m × A/0.1 T
r = 140 × 10⁻⁷ m
r = 1.4 × 10⁻⁵ m
r = 14 × 10⁻⁶ m
r = 14 μm
c
Which three continents contain coal fields that provide evidence for continental drift?
Africa, Antarctica, and North America
Eurasia, Africa, and South America
Antarctica, South America, and Africa
South America, North America, and Eurasia
Answer:
D
Explanation:
its D
If a catalyst was added to the reaction below, which values would be affected? Check all that apply
If a Catatlyst was added the values affected would be 2, 3, 4
What is a cata;lyst?A catalyst is a substance that speeds up the rate of a chemical reaction without undergoing any permanent change itself. It facilitates the reaction by providing an alternative pathway with lower activation energy, which allows the reaction to occur more readily.
Catalysts work by interacting with the reactant molecules and weakening the existing bonds or creating new ones, making it easier for the reaction to proceed.
Catalysts are typically specific to certain reactions and can be used in small amounts relative to the reactants. They play a crucial role in many industrial processes and are essential for efficient chemical transformations.
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Which two chemical equations show double-replacement reactions?
A. C+02 - CO2
B. 2Li + CaCl2 - 2LiCl + Ca
I C. Ca(OH)2 + H2S04 - CaSO4 + 2H20
D. Na2CO3 + H2S - H2CO3 + Na2S
The two chemical equations show double-replacement reactions are Ca(OH)2 + H2S04 - CaSO4 + 2H20 and Na2CO3 + H2S - H2CO3 + Na2S.
What is double replacement reaction?A double replacement reaction have two ionic compounds that are exchanging anions or cations.
From the given options, we can choose the following based on their exchange of anions or cations.
Ca(OH)2 + H2S04 - CaSO4 + 2H20Na2CO3 + H2S - H2CO3 + Na2SThus, the two chemical equations show double-replacement reactions are Ca(OH)2 + H2S04 - CaSO4 + 2H20 and Na2CO3 + H2S - H2CO3 + Na2S.
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should scientist be allowed to do anything that they can?
No, because some scientist are bad and they must have a scientific attitude like honesty, curiosity, open-mindedness, optimistic and more. And they should follow others sometimes because for their own good.
Answer:
No
Explanation:
Science operates in the context of national and international laws, agreements and conventions. It requires scientists to conduct and communicate scientific work for the benefit of society, with excellence, integrity, respect, fairness, trustworthiness, clarity, and transparency.
Potential energy is best defined as which of the following?
A Mass energy
B Energy of Motion
C Stored Energy
D Energy of height
Answer: C. Stored energy
A 45 kg object is lifted vertically at a constant speed to a height of 9.0 m by a 7.5x10² w electric motor. If this motor is 25% efficient in converting electric energy to mechanical energy, how long does the motor take to lift the object?
Answer:
the time taken for the motor to lift the object is 21.17 s.
Explanation:
Given;
mass of the object, m = 45 kg
height through which the object was lifted, h = 9.0 m
electrical power used by the motor, P = 750 W
Efficiency of the electrical motor, n = 25% = 0.25
The electrical energy used by the motor in lifting the object is calculated as;
E = P x t
where;
t is the time taken for the motor to lift the object
E = 750 x t
E = 750t
The electrical energy converted by the motor to mechanical energy is calculated as;
P.E = 0.25(750t)
P.E = 187.5t
Recall, P.E = mgh
mgh = 187.5t
45 x 9.8 x 9 = 187.5t
3969 = 187.5t
t = 3969/187.5
t = 21.17 s
Therefore, the time taken for the motor to lift the object is 21.17 s.
How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 30.0 cmcm in diameter to produce an electric field of 1440 N/CN/C just outside the surface of the sphere
Answer:
1.78×10×10^10 electron
Explanation:
Electric field outside the sphere can be calculated using below expression
E= kq/ r^2..........eqn(1)
Where k= 9 × 10^9 NM^2/C^2
q= charge
E= 1440 N/C
Diameter= 30.0 cm= 0.3 m
r= radius= 0.3/2= 0.15m
If we make q subject of formula from eqn(1) we have
q= Er^2/k............eqn(2)
q= 1440 × (0.15)^2 /(9 × 10^9 )
= 2.85×10^-9C
Total charge is an integer of electron charge , then we can calculate the number of the electron using the expression below
q= Ne
Where
N = number of electron
Making N subject of the formula we have
N= q/e
Where e= electron value= 1.6× 10^-19
N=2.85×10^-9 /1.6× 10^-19
= 1.78×10×10^10 electron