I don’t understand this

a) The planar density expression for FCC (100) is 4/a^2.

    The planar density expression for FCC (111) is 2 / [(sqrt(3) / 2) * a^2].

b)  The planar density for the FCC (100) plane is 24.63 atoms/nm^2.

    The planar density for the FCC (111) plane is  12.32  atoms/nm^2.

a) To derive the planar density expression for the FCC (100) and (111) directions in terms of the atomic radius R, we need to consider the arrangement of atoms in these planes.

FCC (100) Plane:

In the FCC crystal structure, there are 4 atoms per unit cell. The (100) plane cuts through the middle of the unit cell, passing through the centers of the atoms at the corners. Since the atoms at the corners are shared with adjacent unit cells, we only count a fraction of these atoms.

For the (100) plane, we have 2 atoms in the plane, located at the corners of the square, and 1/2 atom at each of the 4 face centers. Thus, the total number of atoms in the plane is 2 + (1/2) * 4 = 4 atoms.

The area of the (100) plane is determined by the square formed by the lattice vectors a and a, which gives an area of a^2.

The planar density (PD) is defined as the number of atoms per unit area, so we divide the total number of atoms (4) by the area (a^2):

PD(100) = 4/a^2

FCC (111) Plane:

In the FCC crystal structure, there are 4 atoms per unit cell. The (111) plane passes through the centers of the atoms at the corners and the center of the face. Similarly to the (100) plane, we need to account for the fraction of shared atoms.

For the (111) plane, we have 1 atom in the plane, located at the corner of the equilateral triangle, and 1/3 atom at each of the 3 face centers. Thus, the total number of atoms in the plane is 1 + (1/3) * 3 = 2 atoms.

The area of the (111) plane is determined by the equilateral triangle formed by the lattice vectors a, a, and a, which gives an area of (sqrt(3) / 2) * a^2.

The planar density (PD) is defined as the number of atoms per unit area, so we divide the total number of atoms (2) by the area ((sqrt(3) / 2) * a^2):

PD(111) = 2 / [(sqrt(3) / 2) * a^2]

b) Now, let's compute the planar density values for the FCC (100) and (111) planes using the atomic radius R = 0.143 nm for Aluminum.

For FCC (100) plane:

PD(100) = 4 / a^2

For Aluminum, the lattice constant a is related to the atomic radius R by the formula:

a = 4R / sqrt(2)

Substituting the given value of R = 0.143 nm:

a = 4 * 0.143 nm / sqrt(2) ≈ 0.404 nm

Therefore, the planar density for the FCC (100) plane is:

PD(100) = 4 / (0.404 nm)^2 ≈ 24.63 atoms/nm^2

For FCC (111) plane:

PD(111) = 2 / [(sqrt(3) / 2) * a^2]

Using the calculated value of a = 0.404 nm:

PD(111) = 2 / [(sqrt(3) / 2) * (0.404 nm)^2] ≈ 12.32 atoms/nm^2

Therefore, the planar density for the FCC (111) plane is approximately 12.32 atoms/nm^2

Thus,

a) The planar density expression for FCC (100) is 4/a^2.

    The planar density expression for FCC (111) is 2 / [(sqrt(3) / 2) * a^2].

b)  The planar density for the FCC (100) plane is 24.63 atoms/nm^2.

    The planar density for the FCC (111) plane is  12.32  atoms/nm^2.

Learn more about FCC https://brainly.com/question/12977980

#SPJ11

Here's the neat, cool way to convert units like this:

-- 1 kilogram  =  1,000 grams

-- 1 meter  =  100 centimeters

So . . . . .

(1000 kg/m³) x (1000 g/kg) x (1 m/100 cm)³ =

(1,000 kg/m³) x (1,000 g/kg) x (1 m³/1,000,000 cm³) =

(1,000 x 1,000 x 1 / 1,000,000) (kg-g-m³ / m³-kg-cm³)  =  1 g/cm³

This is a very large amount of time, approximately \(3.6 x 10^5\) years, which is not feasible for the astronauts.

We can use the conservation of momentum to solve this problem. Initially, the system (two astronauts and the laser) is at rest, so the total momentum is zero. When the laser is fired and the astronaut is propelled towards the shuttle, she gains some momentum in the direction of the shuttle, and the system as a whole gains an equal and opposite momentum.

First, we need to find the momentum gained by the astronaut. We can use the formula for the momentum of a photon:

p = h / λ

where p is the momentum, h is the Planck constant, and λ is the wavelength of the laser light. We are given the power of the laser (121.0 W), but we also need to know the energy of each photon. We can use the formula:

E = hc / λ

where E is the energy of a photon, c is the speed of light, and λ is the wavelength of the laser light. Rearranging this formula, we get:

λ = hc / E

Substituting the values and converting to SI units, we get:

\(λ = (6.626 x 10^-34 J s)(3.00 x 10^8 m/s) / (6.63 x 10^-19 J) = 3.13 x 10^-7 m\)

Using this wavelength, we can find the momentum gained by the astronaut:

\(p = h / λ = (6.626 x 10^-34 J s) / (3.13 x 10^-7 m) = 2.12 x 10^-27 kg m/s\)

This is the momentum gained by the astronaut in one photon.

To find the time it takes for the astronaut to reach the shuttle, we can use the impulse-momentum theorem:FΔt = Δp

where F is the force exerted by the laser, Δt is the time for which the force is applied, and Δp is the change in momentum of the astronaut. We can rearrange this formula to solve for Δt:

Δt = Δp / FThe force exerted by the laser can be found by dividing the power by the speed of light:

\(F = P / c = 121.0 W / 3.00 x 10^8 m/s = 4.03 x 10^-7 N\)

Substituting the values, we get:

\(Δt = Δp / F = (2.12 x 10^-27 kg m/s) / (4.03 x 10^-7 N) = 5.27 x 10^-21 s\)

This is the time it takes for the astronaut to gain the momentum needed to reach the shuttle. However, this time does not include the time it takes for the astronaut to travel the distance to the shuttle. We can use the average velocity of the astronaut to find this time:

v_avg = Δx / Δtwhere Δx is the distance to the shuttle. Substituting the values, we get:

\(v_avg = (39.4 m - 19.7 m) / (5.27 x 10^-21 s) = 3.80 x 10^22 m/s\)

Learn more about the astronauts.

https://brainly.com/question/11244838

#SPJ4

Answer:

Hype

Explanation:

Yyrru

False. The relative humidity will decrease if the mixing ratio drops and the temperature remains unchanged.

Relative humidity is the ratio of the amount of water vapor present in the air to the maximum amount the air can hold at a given temperature, so if the amount of water vapor decreases (due to lower mixing ratio), the relative humidity decreases unless the temperature also decreases.

False. If the temperature remains unchanged and the mixing ratio drops, the relative humidity will decrease. This is because relative humidity is the ratio of the actual amount of water vapor in the air (mixing ratio) to the maximum amount of water vapor the air can hold at a specific temperature. If the mixing ratio decreases while temperature stays constant, the relative humidity will be lower.

To know more about Humidity click here .

brainly.com/question/22069910

#SPJ11

Answer:

Newton's second law states that the acceleration of an object is directly related to the net force and inversely related to its mass. Acceleration of an object depends on two things, force and mass.

Explanation:

here this may help.

Answer:

Initial velocity, u = 23.33 m/s

Explanation:

Given the following data;

Acceleration = 2.5 m/s²

Distance = 4 km to meters = 4000 meters

Time = 0.8 mins to seconds = 0.8 * 60 = 48 seconds.

To find the initial velocity, we would use the second equation of motion;

\( S = ut + \frac {1}{2}at^{2}\)

Where;

S represents the displacement or height measured in meters.

u represents the initial velocity measured in meters per seconds.

t represents the time measured in seconds.

a represents acceleration measured in meters per seconds square.

Substituting into the equation, we have;

4000 = u*48 + ½*2.5*48²

4000 = 48u + 1.25*2304

4000 = 48u + 2880

48u = 4000 - 2880

48u = 1120

Initial velocity, u = 1120/48

Initial velocity, u = 23.33 m/s

The gross weight of the package in kilograms that Donna send to her grandson as birthday present is 7.675 kg.

The weight of the box in which Donna has sent the present (w1)=  0.875 kg. Now  we know, 1 kg = 1000 grams .  So , 0.875 kg = 0.875 * 1000 = 875 grams.

Hence w1=875 grams is the weight of the box in which the present is there.

The weight of the present itself (w2)=6800 grams.

So, the gross weight of the package = w1+w2= 875 +6800 grams = 7675 grams.

So, the gross weight of the package ( the box+the gift) = 7675grams =7675 / 1000 = 7.675 kg.

For further learning about weight , refer to the

https://brainly.com/question/8790553

#SPJ4

The linear expansivity of brass of length 120 m that assumed a new length of 120.05 m when heated to a temperature 100° c​ is 4.167.10⁻¹⁶ 1/K.

Linear expansivity is the ratio of the length increase of a solid specimen to the temperature change. The expansivity (α) of a specimen is given by the formula l2 = l1(1 +), where l1 is the length of the specimen, and l2 is the length of the specimen when the temperature increases by °.

The linear expansion coefficient can be written in SI units as either °C-1 or °K-1. C in this context stands for Celsius, and K for Kelvin. M0L0T0K1 will be the size of the linear expansion coefficient.

Modifying or lengthening is referred to as expansion. When one dimension (length) changes in length in relation to the volume, this is referred to as linear expansion.

When the temperature rises by one degree, a solid's linear expansivity increases by a fractional amount.

calculate the linear expansivity of brass of length 120 m ?

Assuming the temperature change is 100°C.

       α=L−L0/L0- ΔT⇒(1)  Δ Greek value is 4

Given L=120

L0=120.05

T=100°c

 substitute the given values in equation 1 we have

        α=120-120.5/120.05-4(100)

           =4.167.10⁻¹⁶ 1/K

To learn more about linear expansivity refers to:

https://brainly.com/question/14325928

#SPJ1

To start the magnetic field

Answer:

The atomic number of an element represents the number of protons in the nucleus of an atom. For example, carbon has an atomic number of 6, which means it has six protons in its nucleus.

The mass number of an atom represents the total number of protons and neutrons in the nucleus. For example, carbon-12 has a mass number of 12 because it has six protons and six neutrons in its nucleus.

Since the atomic number is equal to the number of protons in an atom, it is not possible for an atom to have 12 protons (atomic number of 12) and a mass number of 10 because the number of protons plus the number of neutrons cannot be less than the atomic number.

Therefore, an atom with an atomic number of 12 must have at least 12 nucleons (protons and neutrons) in its nucleus. The only stable isotope of magnesium, which has an atomic number of 12, has a mass number of 24, meaning it has 12 protons and 12 neutrons in its nucleus.

Answer:

Current, I = 20 Amperes.

Explanation:

Given the following data;

Voltage = 40 V

Resistance = 2 Ohms

To find current flowing through the resistor;

Ohm's law states that at constant temperature, the current flowing in an electrical circuit is directly proportional to the voltage applied across the two points and inversely proportional to the resistance in the electrical circuit.

Mathematically, Ohm's law is given by the formula;

\( V = IR\)

Where;

V represents voltage measured in voltage.

I represents current measured in amperes.

R represents resistance measured in ohms.

Making current (I) the subject of formula, we have;

\( I = \frac {V}{R} \)

Substituting into the formula, we have;

\( I = \frac {40}{2} \)

Current, I = 20 Amperes.

The resultant velocity of the aircraft is determined as 155.24 km/h.

The resultant velocity or any vector is the single vector or velocity that will produce the same effect as both vectors or velocities combined.

Mathematically, the formula for resultant velocity is given as;

Vr² = Va² + Vb²

where;

Vr = √(Va² + Vb²)

Vr = √(150² + 40²)

Vr = 155.24 km/h

Thus, we can conclude that the resultant velocity of the aircraft will be greater than the initial velocity of the aircraft due to effect of the speed of wind.

Learn more about resultant velocity here: https://brainly.com/question/24767211

#SPJ1

Water-based energy generation has the best conversion efficiency (90%) of available power to useable electricity.

Electricity is the collection of physical and perceptual properties linked with the presence and motion of matter that has an electric charge. Both electricity and magnetism are connected to the phenomena of electromagnetic, as defined by Maxwell's equations.

Water can create electricity with a conversion efficiency of around 90%, which is the greatest rate among renewable energy sources. Water energy may have numerous forms: Historically, hydroelectric power was obtained by building extremely large hydroelectric dams and reservoirs, which are still popular in developing nations.

To know more about energy click on the link below:

https://brainly.com/question/13881533

#SPJ4

Maxwell equations are a set of four equations that describe the behavior of electric and magnetic fields. They are named after James Clerk Maxwell, who formulated them in the 19th century.

The equations show how electric and magnetic fields interact with each other and with charges. The equations include Faraday's law of induction, Ampere's law, Gauss's law for electricity, and Gauss's law for magnetism. The displacement current was introduced by Maxwell to explain the behavior of electric fields in changing magnetic fields.

This current was necessary to satisfy Ampere's law, as the traditional current did not account for this behavior. The displacement current is equal to the rate of change of the electric field, thus allowing the total current to satisfy Ampere's law.

Know more about Maxwell equations here

https://brainly.com/question/32131532#

#SPJ11

Answer:

Jupiter and Saturn will come within 0.1 degrees of each other, forming the first visible "double planet" in 800 years.

Explanation:

The 2020 great conjunction is especially rare, the planets haven't been this close together in nearly 400 years, and haven't been observable this close together at night since medieval times, in 1226.

Explanation:

Jupiter and Saturn will come within 0.1 degrees of each other, forming the first visible "double planet" in 800 years. Jupiter and Saturn will be so close today that they will appear to form a "double planet."

Answer:

Suppose two objects of different masses are moving with different velocities in the same direction on a straght-line before collision. After collision, they stick together and move with common (the same) velocity

The acid ionization constant (\(K_{a}\)) for the weak acid HA in the given question for the shared values will be around 0.

We must use the pH and concentration of the acid solution to determine the acid ionization constant (Ka) for the weak acid HA.

The amount to which the weak acid dissociates in water is indicated by the acid ionization constant.

Assumed: pH = 2.93.

HA concentration: 0.190 M.

We will use the following relationship between pH and the number of hydronium ions ( \(H_{3} 0^{+}\) ) to address this issue:

pH equals -log \(H_{3} 0^{+}\)

First, using the provided pH, we must determine the hydronium ion concentration:

\(H_{3} O^{+}\) = \(10^{-pH}\)

\(H_{3} O^{+}\)= \(10^{-2.93}\)

\(H_{3} 0^{+}\) = 7.33 × \(10^{-3}\) M

As we know that HA is a weak acid, it dissociates into its conjugate base

(\(A^{-}\)) and hydronium ions like the following reaction:

\(HA\) ⇄ \(A^{-}\) + \(H_{3} 0^{+}\)

Expression for equilibrium to the above reaction:

\(K_{a\)= (concentration of conjugate base x concentration of hydronium ions)/ concentration of HA

We don't know the concentration of the conjugate base.

But we do know that the solution is very dilute so we can say that the dissociation of the given acid is very less compared to the concentration.

So we can take its value to be 0.

\(K_{a}\) = (0 × \(H_{3} 0^{+}\)) / HA

\(K_{a}\) = 0

So, the acid ionization constant for the given acid will be zero.

Learn more about ionization from the given link:

https://brainly.com/question/1602374

#SPJ4

The acid ionization constant (Ka) for the weak acid is \(1.7 * 10^{-3}\).

To calculate the acid ionization constant (Ka), we need to use the pH value and concentration of the weak acid solution. The pH of the solution indicates the concentration of H+ ions, which is related to the concentration of the weak acid and its dissociation.

The pH can be converted to the concentration of H+ ions using the formula: \([H+] = 10^{(-pH).\)

In this case,\([H+] = 10^{(-2.93).\)

Since the weak acid is not completely dissociated, the concentration of the weak acid ([HA]) can be approximated as its initial concentration, which is given as 0.190M.

The dissociation of the weak acid can be represented as follows:

HA ⇌ H+ + A-

The equilibrium expression for the dissociation is \(K_a = [H+][A-] / [HA]\).

Substituting the values into the equation:

\(Ka = (10^{(-2.93)})(10^{(-2.93)}) / 0.190.\)

Calculating the value gives us:

\(Ka = 1.7 * 10^{-3.\)

Therefore, the acid ionization constant (Ka) for the weak acid is approximately \(1.7 * 10^{-3}\).

Learn more about acid ionization constants (Ka) from the given link:

https://brainly.com/question/31756261

#SPJ11.

Answer:

Option C

Explanation:

The answer is option C or "they convert chemical energy from gasoline into kinetic energy." Electric motors usually require a power source for example a car, you put gasoline in that car which is converted into kinetic energy which allows the motor to operate and run, (enabling you to drive the car) the kinetic energy is then used into you run out of gasoline.

Hope this helps.

The hourly trench production in linear meters is 14.7 m/hour. The bank volume per meter of trench that would be excavated can be found as follows;

Bank Volume = 0.75 m × 0.95

= 0.7125 m³/m

Then, the Bank Volume Per Meter Of Trench = 0.7125 m³/m,

This implies that every 1 m of trench excavated will result in a bank volume of 0.7125 m³. Therefore, the volume of soil to be excavated is 0.7125 m³/m.

If the trench is 0.6 m wide and 2.5 m deep, then the volume of soil required to excavate one linear meter of trench can be calculated as follows

;Volume of Soil Required

= Width × Depth × Bank Volume Per Meter Of Trench

Volume of Soil Required = 0.6 m × 2.5 m × 0.7125 m³/m

= 1.065 m³/m

At 70% job efficiency, the hourly trench production in linear meters can be calculated as follows;'

Production = (60 × job efficiency × Max Depth) / (Swing + Load + Dump + Return) x Volume of Soil Required

Production = (60 × 70% × 5.0 m) / (15 + 10 + 20 + 30) x 1.065 m³/m

Production = 14.7 m/hour

Therefore, the hourly trench production in linear meters is 14.7 m/hour.

To know more about linear meter visit:

https://brainly.com/question/32905153

#SPJ11

Answer:

the exact center of its mass

Answer:

opposite

Explanation:

Answer:

I don't get what you mean

Explanation:

AND HI AGIAN

Answer:

because 2 is the highest mark the highest the ball can go is 2

Explanation:

The radius of the cone with surface area of 2400 m^2 and height of 25 m is approximately 11.8471 m.

To use the false position method, we need to find two initial guesses such that S is less than and greater than 2400 m^2, respectively. We can start with r = 10 m, which gives S = 825.66 m^2, and r = 15 m, which gives S = 1788.85 m^2.

Next, we can apply the false position method to find the value of r that gives S = 2400 m^2. Let xr be the value of r at the nth iteration, then the formula for the false position method is:

xr+1 = xr - ((S(xr) - 2400) * (xr - xl))/(S(xr) - S(xl))

where xl and xr are the values of r that give S less than and greater than 2400 m^2, respectively. We can use the formula to find xr as follows:

x0 = 10, xl = 10, xr = 15, S(xl) = 825.66, S(xr) = 1788.85

x1 = 15 - ((1788.85 - 2400) * (15 - 10))/(1788.85 - 825.66) = 11.84

S(x1) = pi * 11.84 * sqrt(11.84^2 + 25^2) = 2401.05

x2 = 11.84 - ((2401.05 - 2400) * (11.84 - 10))/(2401.05 - 825.66) = 11.847

S(x2) = pi * 11.847 * sqrt(11.847^2 + 25^2) = 2399.89

x3 = 11.847 - ((2399.89 - 2400) * (11.847 - 10))/(2399.89 - 825.66) = 11.8471

S(x3) = pi * 11.8471 * sqrt(11.8471^2 + 25^2) = 2400.01

Therefore, the radius of the cone with surface area of 2400 m^2 and height of 25 m is approximately 11.8471 m.

To learn more about radius, refer below:

https://brainly.com/question/13449316

#SPJ11

The experiment describes the measurement of a diffraction pattern produced by a laser beam incident on a fish within a fish tank. Here, the entire path of the laser was in water and tissue with an index of refraction close to that of water.

Here, d1 is the distance between the laser beam source and the fish, and d2 is the distance between the fish and the screen.So,\($$d_2 = b - d_1$$\) Given that, d1 = 30 cm Let's say that, λ in air = λ Since, the entire path of the laser was in water and tissue with an index of refraction close to that of water. Therefore, the wavelength in water, λ′ is given by\(:$$λ′ = λ/n$$\) where n is the refractive index of water.So, the distance spanned by the diffraction spot as it moved back and forth is:\($$d_2 = b - d_1 = λ′d(n+1/2)$$\)In 100 words, the distance spanned by the diffraction spot as it moved back and forth is given by d2 = λ′d(n+1/2), where d is the distance between the fish and the screen, n is the order of diffraction, λ′ is the wavelength of the laser beam in water and n is the refractive index of water.

Here, the experiment describes the measurement of a diffraction pattern produced by a laser beam incident on a fish within a fish tank, so the properties of the diffraction pattern were thus determined by the wavelength in water. Hence, the diffraction pattern will appear larger on the screen when the screen is in the water.

To know more about Diffraction visit-

https://brainly.com/question/12290582

#SPJ11

The voltage across the capacitor 11 ms after closing the switch is  11 ms.

To solve this problem, we will use the time constant (τ) of the RC circuit, which is given by the product of the resistance (R) and the capacitance (C):

τ = RC

Since the capacitor is initially uncharged, the voltage across it (Vc) at time t is given by:

Vc = V0(1 - e^(-t/τ))

Where V0 is the voltage of the battery.

At time t = 11 ms, the switch is closed, and the capacitor begins to charge. We are asked to find the voltage across the capacitor at this time.

Since the switch is closed, the resistor is in the circuit, and we need to know its value to calculate the time constant.

However, we are not given the value of the resistor, so we cannot solve the problem with the information given.

We need either the value of the resistor or the time constant to calculate the voltage across the capacitor at 11 ms.

For such more question on voltage:

https://brainly.com/question/1176850

#SPJ11

The temperature change produced when 0.35 kg of water is heated using 9600 J is 6.34 °C.

What is Specific Heat Capacity?

Specific heat capacity is the amount of heat energy required to raise the temperature of one unit of mass of a substance by one degree Celsius (or one Kelvin). It is a measure of the substance's ability to store heat energy. The specific heat capacity is a physical property of the substance and is usually denoted by the symbol c.

The amount of heat required to raise the temperature of a substance is given by the formula:

Q = mcΔT

where Q is the amount of heat energy transferred, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.

In this problem, we are given:

m = 0.35 kg (mass of water)

c = 4200 J/kg/°C (specific heat capacity of water)

Q = 9600 J (amount of heat energy transferred)

We can rearrange the formula to solve for ΔT:

ΔT = Q/(mc)

Substituting the given values, we get:

ΔT = (9600 J) / (0.35 kg x 4200 J/kg/°C)

ΔT = 6.34 °C

Learn more about Specific Heat Capacity from given link

https://brainly.com/question/27991746

#SPJ1

Answer:

A 70 kg box is slid along the floor by a 400 n force. The coefficient of friction between the box and the floor is 0. 50 when the box is sliding