A lab technician uses laser light with a wavelength of 640 nm to test a diffraction grating. When the grating is 40.8 cm from the screen, the first-order maxima appear 6.00 cm from the center of the pattern.

The edge length of a unit cell is calculated to be 50,600 pm if the barium metal has a body-centered cubic structure.

The edge length of a unit cell can be determined by using the formula of density as follows;

ρ = (Z × M) / Avogadro's number × a³

In this equation ρ represents density, M represents the atomic mass, a illustrates the edge length of a unit cell and Z represents the number of atoms in a unit cell which is equal to 2.

Substituting the values in this equation to determine the edge length of a unit cell as follows;

3.51 = 2 × 137.33 / (6.022 × 10^23) × (a³)

3.51 = 274.66 / (6.022 × 10^23) × (a³)

3.51 × (6.022 × 10^23) / 274.66 = a³

a = 5.06 × 10^-8 m

Converting m to pm as follows;

as 1 m = 1 × 10^12

Therefore; 5.06 × 10^-8 m = 50,600 pm

Hence 50,600 pm is the edge length of a unit cell.

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A gust of wind creates ripples in the ocean, then the frequency of these ocean waves will be 1.4 Hz.

The percentage of waves that transfer a fixed point in a unit of time is known as the frequency in physics. It is the frequency or vibrations that a body in periodic motion perceptions in a unit of time. When a body in periodic motion moves through a sequence of incidents or positions before returning to its initial state, it is believed to have experienced one cycle or one vibration.

As per the given data mentioned in the question,

Frequency = speed/wavelength

Speed = 6.65 cm/s

Wavelength = 4.7 cm

F = (6.5 × 10⁻²)/(4.7 × 10⁻²)

F = 1.4 Hz

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The elastic potential energy of the same spring when it is stretched by 12 cm is 180 J.

What is elastic?
Elasticity in physics and material science refers to a body's capacity to withstand a force that causes distortion and to recover its original dimensions after the force has been removed. When sufficient loads are applied, solid objects will deform; if the substance is elastic, this same object will revert to its original size and shape after the loads have been removed. Unlike plasticity, which prevents this from happening and causes the object to stay deformed, For various materials, the physical causes of elastic behaviour can vary greatly. When forces are applied, the atomic lattice in metals changes in size and shape. The lattice returns to its initial lower energy state when forces are removed.

The elastic potential energy of a spring is given by the equation:
PE = 1/2 kx^2

Where k is the spring constant and x is the amount of stretching. In this case, k is a constant since it is the same spring and x is the amount of stretching, which is 12cm. Substituting these values into the equation gives:

PE = 1/2 (20 J/8cm^2)(12cm)^2
= 180 J
Therefore, the elastic potential energy of the same spring when it is stretched by 12 cm is 180 J.

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No, as she kept the box a safe distance from her body. As closely as you can, hug the load to your body.

Lift gradually by extending your hips and knees (not your back). As you raise, keep your back straight and avoid twisting. Hold the load at the level of your belly button, as near to your body as you can.

Keep the burden as near to your body as you can, if at all possible. Perhaps this is preferable to fiercely clutching it in your hands. As opposed to either entirely flexing your back (stooping) or fully flexing your hips and knees (full/deep squatting), it is ideal to slightly bend your back, hips, and knees at the beginning of the lift.

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The flow waveform pattern that provides the shortest inspiratory time (TI) of all the available flow patterns with an equivalent peak flow rate setting is Constant.

A wave is the predictable, planned movement of disturbances from one place to another. The most well-known waves are those that flow across the surface of water, but there are also waves in sound, light, and the motion of subatomic particles. In the simplest waves, the disturbance oscillates periodically (see periodic motion) with a defined frequency and wavelength. Mechanical waves, like sound, need a medium to flow through, in contrast to electromagnetic waves, which need not and can move in a vacuum (see electromagnetic radiation). How a wave moves across a medium depends on its properties.

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The speed of the projectile F= μο[tex]i^{2}[/tex]/2π  ㏑(1+ W/r)i^.

The projectile's path between y+dy should be considered. Equation is used to determine the magnetic force acting on the segment as well as the magnetic field of each semi-infinite wire (the top rail is known as wire 1 and the bottom rail as wire).

The field (in the region between the wires) set up by wire 1 is into the paper (the "k" direction), and that set up by wire 2 is also into the paper. The current. in rail. 1. is in the "+ i." direction, and. the current. in rail 2 is in the. " i" direction. The force element (a function of y) acting on the segment of the projectile (in which the current runs in the − j^ direction) is provided below. The coordinate. origin is  at the. bottom of the. projectile.

d F = d F1 +dF2 = idy(− j^)× B1 +dy(− j^ )× B2 =i[B 1 +B 2 ] i dy

F= μο[tex]i^{2}[/tex]/2π  ㏑(1+ W/r)i^.

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According to the given statement the percent yield is closest to 17%

Additionally, the primary distinction between the two would be that molar mass provides the mass of the a mole of a certain material. In contrast, molecular weight refers to a substance's molecule's mass. While molar mass as well as molecular weight have distinct definitions and measurement systems, their values are equivalent.

Briefing:

How to calculate the percentage yield

The reaction between  Li3N(s) and LiH(s) is given as:

Calculate the moles of Li3N

Moles = Mass/Molar mass

Moles = 70/35

Moles = 2 moles

You can see from the reaction the 1 mole of Li3N produces 3 moles of LiH, making the total amount of LiH 6 moles.

Determine the mass of LiH (theoretical yield)

Mass of LiH = 6 * 7.95

Mass of LiH = 47.7g

%yield = actual/theoretical * 100

%yield = 8/47.7 * 100

%yields = 16.77%

Hence the percent yield is closest to 17%

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It would take the probe minimum 8.5 years to reach a distance of 7 AU (1 AU = 150 million km).

The answer to this question depends on many factors, such as the probe's speed, the asteroid's mass, and the asteroid's size. Assuming that the probe is traveling at a speed of 10 km/s and that the asteroid's mass is 5x10^15 kg, the journey will take approximately 8.5 years.

However, this assumes a minimum energy direct trajectory, meaning that the probe would need to make a few course corrections to ensure it stays on the correct trajectory. This could cause the journey to take much longer than 8.5 years. Additionally, the size of the asteroid could impact the journey time, as a larger asteroid could cause the probe to need to make more course corrections.

In conclusion, the journey time for a space probe to travel to an asteroid with a radius of 7 AU using a minimum energy direct trajectory will depend on several factors. However, the journey time could be significantly increased if the probe requires more course corrections or if the asteroid is larger.

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The velocity profile u(y) is defined as V = (alpha)*g*sin(alpha)*h^3/3M, where u is the velocity measured parallel to the plate and y is measured perpendicular to the plate. The air just slightly shear stresses the fluid.

Velocity is a vector measurement of an object's rate of motion and direction of motion. The magnitude and direction must therefore be understood in order to calculate the velocity according to this criterion. It is possible to describe shearing stress, also known as shear stress, as "a type of stress that acts coplanar with cross section of material." Shear forces resulted in shear stress. They are a pair of forces that have the same magnitude and are directed in the opposite direction and operate on opposite sides of a body. A vector quantity is shear stress.

Alpha = g*sin(alpha)*h2/2M [y - y^3/3h^2]

V = (alpha)*g*sin(alpha)*h2/2M

Alpha = g*sin(alpha)*h^3/3M

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Earth’s acceleration toward the skydiver is much smaller than the acceleration of the skydiver

Define acceleration

Acceleration is the rate at which velocity, both in terms of speed and direction, varies over time. When anything moves faster or slower in a straight line, it is said to have been accelerated.

Your descent to the ground quickens as you plummet. This acceleration will keep going until the drag from her falling speed due to wind resistance equals the acceleration caused by gravity. He should keep accelerating downward because air resistance, also known as drag force, is usually far smaller than the normal force of a body. She will reach "terminal velocity" when these forces balance each other out, at which point she will stop accelerating.

He will thereafter fall at the same rate until he activates his chute, however his initial acceleration is brought on by acceleration due to gravity.

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Linda, a biker, is moving along a circular path at a constant speed of 10 km/h. In a neighboring arena kelvin, another biker, is moving along a circular path at a constant speed of 12 km/h. If the acceleration of the two bikers is the same, then Kevin’s circular path has a bigger radius than Linda’s path.

Speed is the pace at which an item moves along a route in time, whereas velocity is the rate and direction of movement. In other words, velocity is a vector, whereas speed is a scalar number.

Given that,

Linda, a biker, is moving along a circular path at a constant speed of 10 km/h.

kelvin, another biker, is moving along a circular path at a constant speed of 12 km/h.

As we know,

acceleration (a) = V²/r

For Linda, a₁ = (10)²/r₁

For Kelvin, a₂ = (12)² /r₂

So, a₁/a₂ = [(10)²/r₁] × [r₂/(12)²]

or, a₁/a₂ = 0.694 r₂/r₁

or, r₁ = 0.694 r₂      [ As, acceleration is same]

Kevin’s speed is higher, the radius of his path must also be higher to maintain the same ratio. Therefore, Kevin’s circular path has a bigger radius than Linda’s path.

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The complete question is as follows:

Linda, a biker, is moving along a circular path at a constant speed of 10 km/h. In a neighboring arena Kevin, another biker, is moving along a circular path at a constant speed of 12 km/h. If the acceleration of the two bikers is the same, what can you infer?

A) The centripetal force on Kevin is higher than that on Linda.

B) The centripetal force on Linda is higher than that on Kevin.

C) Kevin’s circular path has a bigger radius than Linda’s path.

D) Linda’s circular path has a bigger radius than Kevin’s path

A 10-v battery with just a 100- resistor placed across its terminals will conduct 0.1 A of current.

When a patterns is made to enable continuous movement of electric charge, a circuit is produced. A current seems to be the continuous passage of an electric charge thru the electrodes of a circuit; it is frequently referred to as a "flow," like a liquid might travel through with a straight tube.

Use Ohm's law

V = IR

where voltage (V), current (I), and resistance (R)

so,

I = V / R

I = 10 / 100

I = 0.1 A

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The complete question is-

How much current will flow through a 10-V battery with a 100Ω resistor connected across its terminals?

A. 0.1A

B. 1.0A

C. 0

D. 1000A

According to general principles, the object distance shows that the light rays coming from the object are parallel to one another, giving rise to f=-4.221.

A small, often straight-moving light beam is called a ray. A ray is represented by the light beam of a laser or laser pointer. A ray of light travels in a straight line until it hits an object, like a mirror or perhaps the boundary between two materials, per the ray model of light.

Small light beams called rays travel in a straight line as electromagnetic waves. Light always moves in a straight line, despite the fact that reflection and refraction can alter the direction of its speed.

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A transparent oil with refraction index 1.24 spills on the surface of water  Assuming the maximum occurs in the first order, Then the thickness of the oil slick 271 nm

Given refraction index is 1.24

The formula to apply for find the maximum for this thin film is

2nt = mλ

(2)(1.29)t = (1)(700 X 10-9)

t = 2.71 X 10-7 m   which is 271 nm.

Light travels more slowly at higher refractive indices, changing direction within a material with a correspondingly greater degree. This means that lenses made of materials with higher refractive indices can bend light more strongly and have lower profiles. A refractive index of 1.5 applies to glass. In other words, the speed of light in glass is not independent of the color of the light and is 1.5 times slower than in a vacuum.

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For ne to form a liquid at low temperatures, an intermolecular force known as London dispersion forces must be present.

What are intermolecular forces ?

Different sections of a molecule may have a positive or negative charge, which can lead them to arrange into particular forms in a solid. These intermolecular forces are what draw molecules together. The melting and boiling points of a substance depend on the strength of intermolecular forces.

Neon is a noble gas, an inert gas. The London dispersion force exists between them as an intermolecular force. Think of two Ne atoms that are close to one another. Due to their rapid speed, electrons eventually become asymmetrical in their distribution. London dispersion forces, which are transient dipoles caused by unequal electron distributions, are the only intermolecular forces it is capable of showing. The ensuing London dispersion forces can provide weak attractions between neon atoms because neon has electrons. Neon is a monatomic gas that exists. In other words, each neon atom is self-contained and does not interact chemically with any other atoms. As a result, neon's electron distribution can be said to be symmetrically undisturbed, making it nonpolar.

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The final velocity of the two vehicles is 37.5 kph and the initial kinetic energy lost is 0.25Joule

a) Prior to and following the impact, momentum is preserved as follows:

3000×50 = 4000×X

X = 37.5 kph

afterward, 37.5km/h is 10.4166m/s so it’s 4000*10.4166²/2 or about 217000 Joule

so 73000 Joule were lost in the collision

b) The portion lost is calculated as the difference between the kinetic energy before and after the collision, divided by the initial energy:

(1/2×3000×50² - 1/2×4000×37.5²) / (1/2 × 3000 × 50²) = 0.25 Joule

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The force exerted by each wire on the other is 2.646N and it is away from each other.

The distance between the parallel power lines is 40cm and they are of a length of 270m each.

The current in the power line is 140A.

The force on each power line due to another can be given by,

F = uI₁I₂L/2πr

Where,

I₁ and I₂ are the current in the line,

L is the length of the wire,

r is the distance between them,

Putting values,

F = 4 x π x 10⁻⁷ x 140 x 140 x 270/2 x π x 0.4

Solving further,

F = 2.646 N.

The force will be away from each other because the current is in same direction. The magnitude of the force will remain same, whatever direction of the current may be.

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Answer:

C) The right not to be put in double jeopardy.

Explanation:

There was other sources that stated that too, I just chose the image below to make you more confident with ""C" being the right answer.

The point that the axis of rotation passes through in the pencil of length 15.0 cm and mass 10.0 g is point B.

The free body diagram of the pencil that rotates about an axis perpendicular to the plane of the figure is shown in the image attached below.

N = Normal force

mg = Weight

C = Center of mass point

f = Frictional force

The weight of the pencil acts in vertically downward direction at the center of mass of the pencil, that is, at point C. Since, the pencil touches the surface at point B, the force due to weight of the pencil produces a torque and makes the pencil rotate about point B.

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As the voltage is increased, the power losses would decrease.

We now that the term power loss has to do with the loss that occurs as a result of the heating effect of current. The transmission of power at high voltage tends to reduce the power losses that accompanies the transmission of power at a lower voltage and a high current.

As such, when we have the operating voltage of a power line is increased from 300 kV to 600 kV we can see that the voltage has doubled and this would mean that the transmission is now at a much higher voltage which would reduce the power losses even further.

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The different words used to match the given definitions are acceleration, velocity, friction, weight, inertia, magnitude.

1. Acceleration is a measure of how quickly the velocity is changing

2. Velocity is speed in a given direction

3. Friction is the force that resists the movement of one object against another

4. On an object weight is the measure of pull of gravity

5. Inertia is the tendency of an object to resist change in motion

6. Magnitude is the size.

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If two people start at the same place and walk around a circular lake in opposite directions with angular speed of 1.7 × 10−3 rad/s and 3.4 × 10−3 rad/s, they will meet after 20.5 minutes.

ω = θ / T

ω = Angular velocity

θ = Angular distance

T = Time period

ω1 = 1.7 * 10⁻³ rad / s

ω2 = 3.4 * 10⁻³ rad / s

θ = ω T

Let the angular distance covered by both person be θ1 and θ2. Since they start at same point, when they meet the sum of their total angular distances will be 360° which is 2π in radians.

θ1 + θ2 = 2 π

ω1 T + ω2 T = 2 π

T = 2 π / ( ω1 + ω2 )

T = ( 2 * 3.14 ) / ( ( 1.7 * 10⁻³ ) + ( 3.4 * 10⁻³ ) )

T = 1.2314 * 10³ s

T = 1231.4 s

T = 20.5 min

Therefore, they will meet after 20.5 minutes.

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The magnitude of velocity  will be  Δ=5.2 m/s.

What are vector quantities?

Any quantity which is defined by its magnitude and direction both are called as the vector quantities.

Now the data given in the question will be given as:

V(a) = 3 m/s

θ =  north of east

V(b) = 6 m/s

θ =  south of east =  360-40=320 north of east

Now we will find the x and y component of V(a)

V(ax) = V(a) cosθ

V(ax) = 2.82m/s

V(ay) = V(a)Sinθ

V(ay) = 1.03 m/s

Now we will find the x and y component of V(b)

V(bx) = V(b) cosθ

V(bx) = 4.6 m/s

V(by) = V(b) sinθ

V(by) = -3.86 m/s

Now change in velocity will be

ΔV = V(b) - V(a)

ΔV = 1.78 i - 4.89 j

The magnitude of these vectors:

ΔV = 5.2 m/s.

Therefore the magnitude of the V will be 5.2 m/s.

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Option C is correct because moving one of the objects closer by 3 m increases the gravitational force between two objects that are 15 m apart by 1.

All material objects in the universe are subject to the force of gravity, also known as gravitation. The force of gravity tends to draw any two non-zero mass objects or particles toward one another. Subatomic particles and galaxy clusters are both affected by gravity, as are objects of all sizes.

The earth's gravitational pull on a body is known as gravitational force. As an illustration, consider how the gravitational attraction of a tree causes its leaves and fruit to fall to the earth.

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The entire trip is 480 miles.

How many miles is the entire trip?

Using Pythagoras theorem,

160²+120²= √40000 = 200

What is Pythagoras theorem?

In mathematics, the Pythagorean Theorem or Pythagorean Theorem is the fundamental relationship in Euclidean geometry between the three sides of a right triangle. It states that the area of ​​a square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation for the lengths of sides a, b and hypotenuse c and is often called the Pythagorean equation.

This theorem is named after the Greek philosopher Pythagoras, who lived around 570 BC. he was born This theorem has been proven countless times in many different ways. The proofs vary and include both geometric and algebraic proofs, some thousands of years old.

If the Euclidean space is expressed in the Cartesian coordinate system of analytic geometry, the Euclidean distance satisfies the Pythagorean relation. That is, the square of the distance between two points is equal to the sum of the squares of the differences in each coordinate between the points.

Therefore, The entire trip is of 480 miles.

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The fraction of atmospheric pressure at sea level is 0.047.

The stress present in the Earth's environment is known as atmospheric pressure, commonly referred to as barometer strain. One zero one,325 Pa, also known as 1013.25 millibars, 760 mm Hg, 29.9212 inches Hg, or 14.696 psi, is the measure of stress used to describe the same old environment.

The atmospheric sea level is known as

P sea level = P atm = 1.01325 × 10^5 N/m^2

Now pressure at the bottom of empire state will be

P1 = 1.01325 × 10^5 N/m^2

Pressure at the top of empire state will be:

P2 = P1 - rho × g × h

rho = density of air = 1.29 kg/m^3

g = 9.81 m/sec^2

Given:

h = height of empire state = 380 m

P2 = 1.01325 × 10^5 - 1.29 × 9.81 × 380

P2 = 96516.138 N/m^2

So,

Delta P = P1 - P2 = 1.01325 × 10^5 - 96516.138

Delta P = 4808.862 N/m^2

So fraction will be:

N = Delta P / P sea level

N = 4808.862/1.01325 × 10^5

N = 0.04745 = 4.745 × 10^-2

Hence in two significant figures

N = 4.7 × 10^-2 = 0.047

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The recoil (springing or flying back of the gun when shots are fired) momentum of a gun is the same as the momentum of the bullet it fires.

option C is the correct answer.

The principle of conservation of linear momentum states that in an isolated system, the sum of the initial momentum of the system is equal to the sum of the final momentum of the system.

Mathematically, the principle of conservation of linear momentum is written as;

Pi = Pf

where;

m₁u₁ = m₂u₂

where;

Thus, based on the principle of conservation of linear momentum the final momentum of the gun will always be equal to the final momentum of the bullet.

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The average force the ball exerts on the racket is 200 N and  the ratio of this force to the weight of the ball is  102.04.

What do you mean by force?

A force is a push or pull that an object feels as a result of interacting with another thing. Each time two things come into contact, a force is applied to each one of them. When the interaction is finished, the force is no longer sensed by the two objects.

As given in the question,

The weight of the ball = 0.200 kg

Initial velocity = 40 m/s

Time in contact = 40 ms = 0.04 s

a) From the formula of impulse, we can write as:

Impulse (J) = The change in momentum

{since, Impulse (J) = Ft}

Ft = P                          

Ft = mv  

Here, F = force, t = time, P = momentum, m = mass, v = velocity

So, the average force was exerted on the racket can be calculated as:

F(avg) =  mv/t

putting the value from  the question,

F(avg) = (0.200 kg)(40 m/s)/(0.04 s)

F (average) = 200 N

b)  The weight of the ball can be calculated as:

W = mg

Here, W = weight, m = mass, g = gravitational constant

W = (0.200 kg)(9.8 m/s2)

W = 1.96 N

The ratio between the force and weight of the ball can calculated as: F(avg)/W  = 200 N/1.96 N

                = 102.04

Hence, the answers for a and b are 200 N and 102.04 respectively.

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The gravitational force between two very large metal spheres in outer space if the mass of each sphere were halved is 14 N

F = G m1 m2 / r²

F = Gravitational force of attraction

G = Gravitational constant

m1, m2 = Masses of both spheres

r = Distance between the spheres

m1' = m1 / 2

m2' = m2 / 2

F' = G m1' m2' / r²

F' = G ( m1 / 2 ) ( m2 / 2 ) / r²

F' = G m1 m2 / 4 r²

F' = F / 4

F' = 56 / 4

F' = 14 N

Therefore, the force is 14 N

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The mass of the star of the distant solar system is 82 * 10²² kg and the mass of the planet of the distant solar system is 8.58 * 10²⁵ kg

g = G M / r

g = Acceleration due to gravity

G = Gravitational constant

M = Mass of star

r = Distance between both bodies

g = 63.6 m / s²

G = 6.67 * 10⁻¹¹ N m² / kg²

r = 8.6 * 10¹¹ m

Ms = 63.6 * 8.6 * 10¹¹ / ( 6.67 * 10⁻¹¹ )

Ms = 82 * 10²² kg

F = G M m / r²

F = m g

Equating,

m g = G M m / r²

With the above equation, we can find the mass as:

Mp = g r² / G

Mp = 63.6 * ( 1.8 * 10⁷ / 2 )² / 6.67 * 10⁻¹¹

Mass of particle = 8.58 * 10²⁵ kg

Therefore the mass will be equal to 8.58 * 10²⁵ kg

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