To make a glass marble, cm3 of molten glass is poured into a mold. Jennet finds the circumference of the marble using the steps below.
V = 4/3Ïr3
1/6Ï =4/3Ïr3 1/8 = r3 r = 1/2cm
C = Ïr2
C = 1/4Ï cm2

Answer: Without an image or diagram of the assembly shown, it's difficult to provide a specific solution. However, we can provide some general guidance on how to approach the problem.

To determine the maximum value of the average normal stress in each link, you'll need to use the formula for average normal stress:

σ = F/A

where σ is the average normal stress, F is the force applied, and A is the cross-sectional area of the link.

First, you'll need to determine the forces in each link. This can be done using the equations of equilibrium for the entire assembly and for each joint. Once you have the forces in each link, you can use the formula above to determine the average normal stress.

For the pins, you can assume that the stress is uniform across the cross-sectional area of the pin. The maximum average normal stress will occur at the section of the pin with the smallest cross-sectional area.

Again, without more specific information or a diagram, it's difficult to provide a more detailed solution.

The source of both the light and sound is the lightning. Light travels much faster than sound, so when you see the lightning, the sound is still travelling towards you. The speed of sound is 340m/s, so the lightning is about 1020m (340m/s * 3s) away from you.

Light is a form of energy that is visible to the human eye. It is a type of electromagnetic radiation, which is a form of energy that consists of electric and magnetic fields. Light is a form of energy that travels in waves and is made up of different colors. It is made up of the colors of the rainbow, which are red, orange, yellow, green, blue, indigo, and violet. Light can travel through a vacuum, meaning it does not need any matter to travel through. Light is one of the fundamental forces of nature and is essential for life on Earth. It is used in a variety of ways, from powering life and growth to providing humans with vision and communication. Light is also used in a variety of technologies, such as cameras, telescopes, and lasers.

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Using the formula for the flux of a vector field through a sphere, we can then compute the net outward flux across the boundary of d.  ∇⋅f = [tex](1/2)(x^2+y^2+z^2)^{-3/2}(2x,2y,2z)[/tex]

To use the divergence theorem to compute the net outward flux of the vector field f across the boundary of the region d, we need to first calculate the divergence of f at a point within d. We can do this by taking the partial derivative of f with respect to each of the three spatial dimensions and evaluating the result at the center of d.

Once we have the divergence of f at a point within d, we can use the divergence theorem to relate the divergence at that point to the flux through any closed surface enclosing d. The net outward flux across the boundary of d will be the negative of the sum of the fluxes through any closed surfaces enclosing d, where the flux through a surface is proportional to the negative of the divergence of f at the center of the surface.

To compute the flux through a sphere of radius centered at the origin, we can use the formula for the flux of a vector field through a sphere, which is given by:

F = (4/3)πr3(∇⋅f)f

In our case, f is the vector field given by [tex]f(x,y,z) = (x^2+y^2+z^2)^(-1/2).[/tex] To calculate the divergence of f at the center of the sphere, we can take the partial derivative of f with respect to each of the three spatial dimensions and evaluate the result at the center of the sphere. This gives us:

∇⋅f = [tex](1/2)(x^2+y^2+z^2)^{-3/2}(2x,2y,2z)[/tex]

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Magnitude of the friction force exerted on the ladder by the floor is equal to the product of the coefficient of static friction and the normal force exerted by the floor on the ladder.

When the ladder leans against the wall, it exerts a force on the wall perpendicular to it, called the normal force. The floor also exerts a force on the ladder perpendicular to it, which is equal and opposite to the normal force exerted by the ladder on the floor.

In order for the ladder to remain stationary and not slip, the friction force between the ladder and the floor must be sufficient to balance the force of gravity acting on the ladder. The coefficient of static friction is a measure of how "sticky" the surfaces are in contact, and determines the maximum friction force that can be exerted.

Therefore, the magnitude of the friction force exerted on the ladder by the floor is given by the product of the coefficient of static friction and the normal force exerted by the floor on the ladder.

Factors involved in determining the friction force between the ladder and the floor.

To find the magnitude of the friction force, we can use the concept of static equilibrium. Since the ladder is not moving, the forces acting on it must be balanced, which means the sum of the forces in the horizontal and vertical directions must be equal to zero.

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The combustion of 200g of C2H5OH releases approximately 2.38 x 10^3 kJ of heat. This is calculated using the given DH value and the stoichiometry of the reaction.

To calculate the amount of heat released, we first need to convert the mass of C2H5OH to moles, which is approximately 3.94 mol. Then, using the DH value of -1234.8 kJ/mol, we can calculate the total amount of heat released as (-1234.8 kJ/mol) x (3.94 mol) = -4865.5 kJ. However, since the reaction produces 2 moles of CO2 and 3 moles of H2O for every mole of C2H5OH combusted, we need to adjust the calculated value accordingly. Therefore, the heat released when 200g of C2H5OH is combusted is approximately 2.38 x 10^3 kJ. In summary, the combustion of 200g of C2H5OH releases a significant amount of heat due to the exothermic nature of the reaction. This heat is released as a result of the formation of CO2 and H2O from the reactants, and the total amount of heat released can be calculated using the DH value and the stoichiometry of the reaction.

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Both Technician A and Technician B are approaching the problem of diagnosing a short circuit in different ways. Technician A is using a self-resetting circuit breaker to replace the fuse, while Technician B is disconnecting and isolating different parts of the circuit one at a time.

Using a self-resetting circuit breaker can be a quick fix for a short circuit, as it will automatically reset itself after tripping.

However, this may not necessarily solve the root cause of the short circuit and may lead to repeated tripping.

On the other hand, Technician B's method of disconnecting and isolating different parts of the circuit can help identify the specific source of the short circuit, allowing for a more targeted and effective solution.
Both methods have their pros and cons and the best approach will depend on the specific situation and the skills and knowledge of the technician.

It is important to carefully consider the root cause of the short circuit and to use appropriate diagnostic tools and techniques to solve the problem effectively.

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In the equation sinθ = λ/a for single-slit diffraction, θ is the phase angle between the extreme rays.

Define diffraction.

Waves spread out as they move through an aperture or around objects, which is known as diffraction. It happens when the aperture's or obstacle's size is of the same order of magnitude as the wave's wavelength. Nearly all of the wave is blocked at very small aperture sizes.

Phase angle is the term used to describe a specific time interval within a cycle that is measured from an arbitrary zero and expressed as an angle. In addition, one of the most crucial aspects of a periodic wave is a phase angle.

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The fluid compartments in the human body are divided into two main categories: intracellular fluid and extracellular fluid. Intracellular fluid is the fluid found inside cells, while extracellular fluid is the fluid found outside cells. The extracellular fluid is further divided into interstitial fluid and plasma.

Of these compartments, the greatest fluid volume is found in the intracellular fluid compartment. This is because the majority of the body's cells are made up of water and the intracellular fluid accounts for approximately two-thirds of the total body water.

However, while the intracellular fluid compartment has the greatest fluid volume, the extracellular fluid compartment is still important as it helps to transport nutrients, waste products, and other substances throughout the body.

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If an object is put into motion in space, it will continue to move in a straight line with a constant speed unless acted upon by an external force. This is due to the absence of air resistance and other forces that typically slow down objects on Earth.

Additionally, the object's motion will be affected by the gravitational forces of nearby celestial bodies, which can cause it to accelerate or change direction.

When an object is put into motion in space, it will continue to move in a straight line at a constant velocity due to the lack of external forces acting upon it. This phenomenon is explained by Newton's first law of motion, also known as the law of inertia. In space, there is no air resistance or friction, which means there are no external forces to slow down the object. Therefore, the object will maintain its constant velocity unless acted upon by another force, such as gravity from a nearby celestial body.

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The tangential velocity (v) of a point on the tip of a fan blade with a diameter of 1 m and an angular velocity (ω) of 2 rad/s can be calculated using the formula:
v = ω * r

where r is the radius of the fan blade. Since the diameter is 1 m, the radius (r) is 0.5 m. Now, we can plug the values into the formula:
v = 2 rad/s * 0.5 m = 1 m/s

So, the tangential velocity of a point on the tip of the fan blade is 1 m/s.

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B. Conduction. Conduction is the process by which heat is transferred through matter by the collision of particles within the material. Heat from the core is transferred through the mantle to the base of the crust by conduction, which is the transfer of energy through physical contact.

Conduction is the process of heat or energy transfer from one material to another. It occurs when particles of a material vibrate, causing them to collide and exchange energy. Conduction can occur through both solid and liquid materials, and is most commonly seen in metals. Heat is transferred through conduction as the particles at the hotter end of a material absorb energy and move faster, while particles at the cooler end lose energy and move slower. This movement of particles results in the heat being transferred from the hotter end to the cooler end. Conduction is commonly used in the design of radiators, cookers and other forms of heating.

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Answer:

Since the penny is a conductor , the charge is located on the surface . Assuming a location very near the surface of the conductor , and therefore it can be treated like an infinite surface , the electric field will be : E = σ ϵ 0 Solve for the surface charge density : σ = E ϵ 0 = ( 2000 N/C ) ( 8.85 × 10 − 12 C 2 / N m 2 ) = 1.77 × 10 − 8 C/m 2

Explanation:

51D is the strength S of the person's eye lens

Define lens's strength

The lens's construction material and the angle at which its curved surface is ground together define the lens's strength. Diopters (D), a unit of measurement for lens strength, represent how much light is bent. The strength of the lens increases with the diopter.

The optical component known as the objective is what collects light from the object under observation and concentrates it to create an actual image.

1/O + 1/I = S

O = 2cm

I = 100cm

S = 1/2 + 1/100

S = 51D

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Ranking: Tin, Silver, Nickel, Iron.

Explanation: The specific heat capacity of each metal determines how much heat is needed to raise its temperature. Since all samples have the same mass, the metal with the lowest specific heat capacity will experience the highest temperature increase. Tin has the lowest specific heat capacity and will thus have the highest temperature. Silver, Nickel, and Iron have progressively higher specific heat capacities and will experience correspondingly lower temperature increases. Therefore, the order of temperature from lowest to highest is Tin, Silver, Nickel, and Iron.

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The type of energy produced by this system is thermal energy. Sunlight is used to heat the air within the solar panels, which in turn heats the copper tubes filled with water. The heated water can then be used for various purposes, such as heating homes or generating electricity through steam turbines.

This process of using sunlight to generate heat is known as solar thermal energy, which is a renewable and sustainable source of energy. Solar thermal systems can be used in a variety of applications, from residential heating to industrial processes. Overall, solar thermal energy is an efficient and eco-friendly alternative to traditional fossil fuels.

In the type of solar energy system you described, sunlight heats the air within solar panels, which then heat copper tubes filled with water. The type of energy produced by this system is thermal energy. Thermal energy is the energy that comes from heat and is generated when the sun's rays are absorbed by the solar panels. The heated air transfers this thermal energy to the copper tubes containing water, subsequently heating the water. In summary, this solar energy system converts sunlight into thermal energy through a process involving solar panels, heated air, and copper tubes filled with water.

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The flux of a vector field, denoted by Φ, is the net outward flow through a given surface S. In this case, the surface is an outwardly oriented open cylinder having radius 1 between two planes.

The flux of the vector field through this cylinder is calculated by integrating the dot product of the vector field with the outward unit normal vector across the surface of the cylinder. In mathematical terms, this is written as: Φ = ∫S (F.n) dS where F is the vector field, n is the outward unit normal vector, and dS is the differential area element.

The integration is performed over the surface of the cylinder. The result is the total flux of the vector field through the cylinder.

In summary, the flux of a vector field through an outwardly oriented open cylinder with radius 1 between two planes can be calculated by integrating the dot product of the vector field with the outward unit normal vector across the surface of the cylinder.

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The capacitance of the capacitor used for recording of voltages due to brain activity in an EEG is 0.00318 Farads or 3.18 millifarads (mF).

The capacitance can be calculated using the formula I = C*dV/dt, where I is the current, C is the capacitance, and dV/dt is the rate of change of voltage over time. Rearranging the formula, we get C = I/(dV/dt).

In this case, the current is given as 100 mA and the frequency of the signal is 0.5 Hz. Since the voltage is given as 10 V, we can calculate the rate of change of voltage over time as 2*[tex]\pi[/tex]*0.5*10 = 31.4 V/s.

Plugging in the values, we get:
C = 0.1 A / (31.4 V/s) = 0.00318 F.

Therefore, the capacitance is 0.00318 Farads or 3.18 millifarads (mF).

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The spring constant (k) of the spring is 110.66 N/m.

To find the spring constant, you can use Hooke's law and the formula for the period of a mass-spring system. The formula for the period (T) is:
T = 2π√(m/k)
Where m is the mass of the object and k is the spring constant. First, you need to find the mass (m) using the weight (125 N) and the acceleration of gravity (9.81 m/s²):
m = weight / g
m = 125 N / 9.81 m/s²
m ≈ 12.74 kg
Next, you can rearrange the formula for the period to solve for the spring constant (k):
k = (4π²m) / T²
Plug in the values:
k = (4π² * 12.74 kg) / (4.63 s)²
k ≈ 110.66 N/m

Summary: A 125 N object vibrating with a period of 4.63 s when hanging from a spring has a spring constant of approximately 110.66 N/m.

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The electric field strength, E, at point P on the axis of the rod due to the rod is given by Coulomb's Law as:E = k*(q/r²)

A field is a geographic area or a specific subject or discipline that is studied in great detail. It refers to an area of knowledge or study that is focused on a specific topic, such as physics, mathematics, engineering, philosophy, or psychology. Fields are often divided into sub-fields or branches in order to focus on a particular aspect. For example, the field of psychology might include the sub-fields of clinical psychology, educational psychology, and developmental psychology.

where k is the Coulomb constant (8.99x10⁹ Nm²/C²), q is the total charge on the rod and r is the distance from point P to the center of the rod.

Therefore, the expression for the electric field strength at point P on the axis of the rod at distance r from the center is:

E = 8.99x10⁹ Nm²/C² * (q/r²)

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The distance is not given, we cannot calculate the moment. Therefore, we cannot answer this question without more information.

Force is an interaction between two objects that causes a change in the motion of one or both objects. It is a vector quantity, meaning it has both magnitude and direction. Forces can be either contact forces, exerted when two objects come into direct contact, or non-contact forces, such as gravity, exerted even when the two objects are not in direct contact.

The moment of force (also known as torque) is equal to the magnitude of the force multiplied by the distance from the point of rotation. Since the magnitude of force is given, the moment about point A can be calculated as follows:
Moment = f×d
where f is the magnitude of the force (20 kn) and d is the distance from point A.
Since the distance is not given, we cannot calculate the moment. Therefore, we cannot answer this question without more information.

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For sharper turns, you should use the hand-over-hand steering technique. This involves pulling the steering wheel down with one hand while the other hand crosses over to pull the wheel further down, allowing for greater control and precision in the turn.

Steering techniques are different methods used by drivers to control the steering wheel of a vehicle in order to safely and effectively navigate turns and corners. Some common steering techniques include:

1. Hand-over-hand steering: This is a basic steering technique that involves gripping the wheel with both hands and pulling down on the wheel with one hand while the other hand pushes up.

2. Hand-to-hand steering: This is another common technique where the driver places their hands at the 9 o'clock and 3 o'clock positions on the wheel and rotates the wheel using both hands to navigate turns.

3. Push-pull steering: This technique involves pushing the wheel up with one hand while pulling it down with the other hand to make turns.

4. Shuffle steering: This technique involves shuffling the hands back and forth on the steering wheel in a smooth and fluid motion, allowing for more precise control and faster reaction times.

5. One-hand steering: This technique is used for slower speed turns and involves using one hand to control the wheel while the other hand is free to operate other vehicle controls.

It's important for drivers to choose the appropriate steering technique based on their driving situation, the speed of the vehicle, and road conditions.

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To determine the kinetic energy of the asteroid just before it hits Earth, we would need to know its mass and velocity. Kinetic energy can be calculated using the formula KE = 0.5 * m * v^2, where KE is the kinetic energy, m is the mass, and v is the velocity of the asteroid.

(a): Without knowing the mass and velocity of the asteroid, we cannot provide an exact value for the kinetic energy. Please provide this information for a specific calculation.
(b): Comparing the energy of the asteroid to the output of the largest fission bomb (2100 terajoules) would require us to know the asteroid's kinetic energy.

Once we have this value, we can compare the two energies and discuss the potential impact on Earth.

Summary: To answer your question, we need to know the mass and velocity of the asteroid to calculate its kinetic energy. Once we have that information, we can compare it to the energy output of the largest fission bomb and assess the potential impact on Earth.

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Answer: 1496.526 kg

Explanation:

Given the kinetic energy of the car is 4.31 x 10^5 J and the given speed is 24m/s both are in SI units so need to change the units

As we know

KE = 1/2 m v^2

We know K. E and V transposing v on the other side the final equation which we get is

m = 2 X (K.E/v^2)

Substituting the given values in the question in the above equation we finally get

m as 1496.526 kg.

Therefore the answer to the above-given question is 1496.526 kg.

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The final velocity of the two freight cars after the collision will be 1.1 m/s.

To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of an isolated system remains constant. In this case, the two freight cars stick together after the collision, so we can consider them as a single system.

The initial momentum of the system is:

pinitial = m₁ × v₁+ m₂ × v₂

where m₁ and m₂ are the masses of the two freight cars, and v₁ and v₂ are their initial velocities. Substituting the given values, we get:

pinitial = 30 000 kg × 2.2 m/s + 30 000 kg × 0 m/s

= 66 000 kg.m/s

After the collision, the two freight cars stick together and move with a common final velocity, which we can calculate using the conservation of momentum principle as:

pfinal = (m₁ + m₂) × vfinal

where vfinal is the final velocity of the combined system. Since the total momentum is conserved, we have:

pinitial = pfinal

Substituting the given values and solving for vfinal, we get:

66 000 kg.m/s = (30 000 kg + 30 000 kg) × vfinal

vfinal = 66 000 kg.m/s / 60 000 kg

= 1.1 m/s

Therefore, the final velocity of the two freight cars after the collision is 1.1 m/s.

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The current when the voltage is 200 volts and the resistance is 12 ohms is 16.67 amps (rounded to two decimal places).

Resistance is the opposition to the flow of electric current, or the opposition to a change in electric potential. Resistance is a fundamental property of electrical circuits and components, and is measured in units of ohms. When a voltage is applied across a resistor, current will flow through it in proportion to the voltage. The amount of current that flows is determined by the resistance, which is a measure of the opposition to the flow of current. Resistance is an important concept in the field of electronics and is used to determine the behavior of circuits and components.

The equation that describes this relationship is I = v/r.
We can use this equation to solve for the current when the voltage is 200 volts and the resistance is 12 ohms.
I = v/r
I = (200 volts) / (12 ohms)
I = 16.67 amps
Therefore, the current when the voltage is 200 volts and the resistance is 12 ohms is 16.67 amps (rounded to two decimal places).

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correct option is b. doubled

the change in energy of an ocean wave when its amplitude changes. An ocean wave initially has an amplitude of 2.5 m and then the amplitude increases to 5.0 m due to a change in weather conditions.

Amplitude is the maximum displacement from its mean position to the extreme position of a particle of the medium in which a wave propagates.

The amount of energy transported by the wave is

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The capacitance, in pf, of a teflon-filled parallel-plate capacitor having a plate area of 1.55 cm² is 48.03 PF

a= 1.55 cm² = 1.55 × 10⁻⁴m²

d = 0.060mm =0.6 × 10⁻³m

determining the value for teflon = 2.1

C = KE₀A/d

  = 2.1 × 8.854 × 10 ⁻¹²× 1.55 × 10 ⁻⁴/ 0.06 × 10⁻³

 =  28.819 × 10 ⁻¹⁶ / 0.06 ×10⁻³

 = 480.32 × 10 ⁻¹³

= 48.03 PF

Dielectric strength of teflon will be 60 × 10⁶ v/m

v = Ed = 60 × 10⁶ × 0.6 × 10⁻³m

          = 36 ×10³

v = 3.6 KV

Thus, the maximum potential of teflon filled parallel-plate capacitor is 3.6KV

The ratio of the magnitude of charge on either of the conductor plates to the potential difference that exists between the conductors is what is referred to as the capacitance of a capacitor. C=QV or Q∝V. The SI unit of capacitance is coulomb per volt or farad (F)

The ratio of a system's change in electric potential to its change in electric charge is known as capacitance. The capacitance of any capacitor can be either fixed or variable, contingent upon its use. It may appear from the equation that "C" is affected by voltage and charge.

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The loudness of the sound from the speaker will be 97.5 dB at a distance of 2.9 mm from the speaker.

The loudness of a sound wave can be measured in decibels (dB) and is related to the power of the wave. The formula to calculate the sound intensity level (SIL) in decibels is SIL = 10 log(I/I₀), where I is the sound intensity and I₀ is the reference intensity, which is usually taken to be the threshold of human hearing, 1 × 10⁻¹² W/m².

To calculate the distance at which the loudness of the sound from the speaker will be 97.5 dB, we can use the formula for sound intensity, which is given by I = P/4πr², where P is the power of the wave and r is the distance from the source.

Since the speaker produces 1 W of power, we can substitute P = 1 W into the formula to get I = 1/4πr².  Setting SIL = 97.5 dB, we have:

97.5 = 10 log(I/I₀)

9.75 = log(I/I₀)

I/I₀ = 10^9.75 = 7.94 × 10⁹

Substituting this value for I/I₀ into the formula for sound intensity and solving for r, we get: 7.94 × 10⁹ = 1/4πr²

r = sqrt(1/(4π × 7.94 × 10⁹)) = 0.0029 m or 2.9 mm.

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The type of nuclear decay that involves the conversion of a neutron to a proton and the accompanying emission of high-speed electrons from the unstable nucleus is beta decay.

In beta decay, a neutron in the nucleus transforms into a proton, and an electron and an antineutrino are emitted from the nucleus. This process helps to stabilize the nucleus and reduce its overall energy.
The type of nuclear decay you're referring to is called "beta minus decay" (β- decay). In beta minus decay, a neutron is converted into a proton, and an electron (high-speed electron called a beta particle) is emitted from the unstable nucleus.

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Angle for third-order maximum of 576 nm yellow light on 1,480 lines per cm grating is approximately 71.8 degrees.

What is the angle in degrees for the third-order maximum of 576 nm yellow light on a diffraction grating with 1,480 lines per centimeter?

To find the angle in degrees for the third-order maximum for yellow light with a wavelength of 576 nm and a diffraction grating of 1,480 lines per centimeter, we can use the formula:

sin θ = (mλ)/d

Where:

θ is the angle of diffraction

m is the order of diffraction

λ is the wavelength of light

First, we need to find the value of d. We know that the grating has 1,480 lines per centimeter, which means that there are 1,480/2 = 740 lines per millimeter. Thus adjacent slits is:

d = 1/740 mm = 0.001351 mm

Next, we can substitute the values given into the formula and solve for θ:

m = 3

λ = 576 nm

d = 0.001351 mma

sin θ = (3 x 576 nm)/(0.001351 mm) = 0.951

θ = sin^-1(0.951) = 71.8 degrees

Therefore, the angle in degrees for the third-order maximum for 576 nm wavelength yellow light falling on a diffraction grating having 1,480 lines per centimeter is approximately 71.8 degrees.

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