Use the kinetic-molecular theory to explain the compression and expansion of gases.

Answer:

When the volume increases or when the temperature decreases

Explanation:

The ideal gas equation states that:

[tex]pV= nRT[/tex]

where

p is the gas pressure

V is the volume

n is the number of moles of gas

R is the gas constant

T is the gas temperature

Assuming that we have a fixed amount of gas, so n is constant, we can rewrite the equation as

[tex]\frac{pV}{T}=const.[/tex]

which means the following:

- Pressure is inversely proportional to the volume: this means that the pressure decreases when the volume increases

- Pressure is directly proportional to the temperature: this means that the pressure decreases when the temperature decreases

The gas pressure inside a container can decrease due to a decrease in gas temperature, an increase in container volume, or the removal of gas particles from the container.

The gas pressure inside a container can decrease due to several factors. The most common reasons include a decrease in the temperature of the gas, an increase in the volume of the container, or the removal of some gas particles from the container.

For example, if we take Charles's law into account which states that the volume of a gas is directly proportional to its temperature at constant pressure, so when the temperature decreases, the volume of the gas also decreases. Thus, the gas particles hit the container walls with less force and less frequently, which leads to a decrease in the pressure inside the container.

Similarly, according to Boyle's law, the pressure of a gas is inversely proportional to its volume at a constant temperature. So, when the volume of the container increases, the gas particles have more space to move around, thus they hit the container walls less frequently, resulting in lower pressure.

Lastly, if some of the gas particles are removed from the container, there would be fewer particles to exert force on the container walls, leading to a decrease in pressure.

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Answer:

[tex]159.2 kg/m^3[/tex]

Explanation:

The mass of the liquid is

m = 1.0 kg

The volume of the cylindrical tank is given by

[tex]V=\pi r^2 h[/tex]

where

r = 0.10 m is the radius

h = 0.20 m is the heigth

Substituting,

[tex]V=\pi (0.10 m)^2 (0.20 m)=6.28\cdot 10^{-3}m^3[/tex]

So now we can find the density of the liquid:

[tex]\rho = \frac{m}{V}=\frac{1.0 kg}{6.28\cdot 10^{-3} m^3}=159.2 kg/m^3[/tex]

Answer:

Because moisture and warmth are crucial to thunderstorms, it makes sense that they would occur more often in the spring and summer, particularly in humid areas such as the southeastern United States.The rising moisture that has lost an electron carries a positive charge to the top of the cloud.

Answer:

187.37 m

Explanation:

The wavelength of an electromagnetic wave is given by:

[tex]\lambda=\frac{c}{f}[/tex]

where

c is the speed of light

f is the frequency

We see that the wavelength is inversely proportional to the frequency: this means that the shortest am wavelength will occur at the highest am frequency, which is

[tex]f=1600 kHz = 1600 \cdot 10^3 Hz[/tex]

And substituting also the speed of light

[tex]c=2.99792 \cdot 10^8 m/s[/tex]

We find the wavelength:

[tex]\lambda=\frac{2.99792 \cdot 10^8 m/s}{1600\cdot 10^3 Hz}=187.37 m[/tex]

Answer:

1.D

2. False

3.True

4.True

5.C

6.B

7.C

8.B

9.A

10.True

11.D

12.B

13.A

If you have any questions more,you can ask me later

Answer:

These are all correct and verified

1.D

2. False

3.True

4.True

5.C

6.B

7.C

8.B

9.A

10.True

11.D

12.B

13.A

Explanation:

I did the exam for Marine Science!

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C. 0.37V. A capacitor of 650x10⁻⁴F that stores 24x10⁻³C has a potential difference of 0.37V between its plates.

The key to solve this problem is using the capacitance equation C = Q/Vᵃᵇ, where C is the capacitance, Q the charge stored in the plates, and Vᵃᵇ the potential difference between the plates.

A 650x10⁻⁴F capacitor stores 24x10⁻³C, clear Vᵃᵇ for the equation:

C = Q/Vᵃᵇ -----------> Vᵃᵇ = Q/C

Solving

Vᵃᵇ = 24x10⁻³C/650x10⁻⁴F = 0.37V

Answer:

c

Explanation:

edge

Answer:

D.

Explanation:

It is D because person A is moving with the train, so they wouldn't experience any pitch change relating to the train's movement.

It sounds normal to people A and B. They're moving with the train, so the horn ON the train isn't moving toward them or away from them.

Answer:

a volcanic winter.

Explanation:

the ash blocks the sun, preventing its heat and as the ash leaves, the sun can shine though. hope this helps

The temporary cooling of the island following a volcanic eruption is likely due to haze-effect cooling, a phenomenon where volcanic ash and gases block out sunlight, thereby lowering the temperature. This effect can last for a year or more, leading to temporary climate changes.

The temporary cooling of the island after a volcanic eruption is most likely due to a phenomenon known as haze-effect cooling. This occurs when a volcano releases large volumes of gases and solids such as sulfur dioxide and ash into the atmosphere. These materials can block out sunlight, thereby causing a drop in temperature.

Volcanic eruptions are natural drivers of climate change influencing the climate over a few years, causing short-term climate changes. An example of this is when the volcanoes in Iceland erupted in 1783, releasing large volumes of sulfuric oxide. This led to haze-effect cooling, which produced some of the lowest average winter temperatures on record in Europe and North America in 1783 and 1784.

This haze-effect cooling usually extends for one or more years before dissipating. So it could be inferred that the cooling on the island is likely temporary and will return to normal once the suspended particles from the eruption have dissipated.

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An atomic bomb is a device that has been used as a nuclear weapon by means of nuclear fission (separation of a heavy nucleus into lighter nuclei). It should be noted that there are also devices that work with nuclear fusion (the union of two nuclei) but until now there are no records of their use for war purposes.

This type of fission bombs release a large amount of energy (in the form of heat and radiation of all wavelengths, including dangerous ionizing radiation) by provocating a sustained chain reaction, after which convective processes (transmission of heat through the air) are produced, causing its characteristic mushroom shape with the expansive wave and destroying everything in its path.

Answer:

The answer would be an Atomic Bomb.

an atomic bomb is  a nuclear weapon in which enormous energy is released by nuclear fission.

Explanation:

That would be Earth, because astronomical unit is defined as distance between Earth and sun.

Hope this helps.

r3t40

Answer: The largest object in the solar system would be the object in the middle because its mass bring smaller object into orbit. in our solar system that would be the Sun.

Explanation:

This physics question involves the concepts of light interference and double-slit experiment. The formula Ym = m*λD/d is used to find the position of bright and dark fringes on a screen. The distances to the 5th bright fringe and 8th dark fringe were calculated as 4.7 cm and 7.6 cm respectively.

The question involves the concept of interference of light, specifically as it pertains to a double-slit experiment. To find the distance from the central bright fringe to other fringes, you can use the formula for the path difference between two waves, given by Ym = m*λD/d, where:

Part A: For the 5th bright fringe, we use m=5 (not counting the central bright fringe). So, y5 = 5 * 525 × 10^-9 m * 75.0/4.15×10^-5 m = 0.047 m or 4.7 cm.

Part B: In the case of dark fringes, the formula changes a bit. For dark fringes, the path difference is given by (m+b)*λD/d , where b=1/2. So for the 8th dark fringe, m=8, and the formula becomes: y8 = (8+1/2) * 525 × 10^-9 m * 75.0/4.15×10^-5 m = 0.076 m or 7.6 cm.

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Answer:

The buoyant force is the pressure of the object being forced upward.  

Weight of the object affects the buoyant force of the submerged object; as weight is added to the object, it will cause the object to sink.  The more weight...the more it will sink.

If the weight is less than the buoyant force, it will cause the object to go up.

If the weight is the same as the buoyant force, the object will stay in the same position.

Explanation:

Your answers are correct. You have to read the plaques in the virtual lab to find the answers. So it shows you read them.

1. billion

2. modern

3. Organism

4. Heights

5. clams

6. flowery

The refractive index is the speed of light in a vacuum over the speed of light in the medium.

The answer is B. the ratio of the velocity of light in a vacuum over the velocity of light in the medium

Answer: Option B: the ratio of the velocity of light in a vacuum over the velocity of light in the medium, n = c/v

Explanation:

When a wave of light enters in some materials, the velocity changes depending on the material, and this is why some times when light enters in something, for example, a glass of water, the "path" of the light changes (and you can see some cool visual effects)

then, we define the refractive index of a medium as:

n = c/v

where n is the refractive index, c is the velocity of the light in the vacuum and v is the velocity of the light in the material, here you can see that n is always greater or equal than 1 ( in the case n = 1, we also have v= c)

Then, the correct option is:

option B:  the ratio of the velocity of light in a vacuum over the velocity of light in the medium

Answer:

the attraction between the solute and solvent is about as strong as the attraction between the solvent particles.

Explanation:

(a) [tex]2.4\cdot 10^{-17} J[/tex]

The De Broglie wavelength of a particle is given by

[tex]\lambda=\frac{h}{p}[/tex] (1)

where

h is the Planck constant

p is the momentum of the particle

We also know that the kinetic energy of a particle (K) is related to the momentum by the formula

[tex]K=\frac{p^2}{2m}[/tex]

where m is the mass of the particle. Re-arranging this equation,

[tex]p=\sqrt{2mK}[/tex] (2)

And substituting (2) into (1),

[tex]\lambda = \frac{h}{\sqrt{2mK}}[/tex] (3)

For an electron,

[tex]m=9.11\cdot 10^{-31}kg[/tex]

In the problem, the electron has a de broglie wavelength equal to the diameter of a hydrogen atom in the ground state:

[tex]\lambda = d = 1\cdot 10^{-10} m[/tex]

So re-arranging eq.(3) we can find the kinetic energy of the electron:

[tex]K=\frac{h^2}{2m\lambda^2}=\frac{(6.63\cdot 10^{-34}Js)^2}{2(9.11\cdot 10^{-31} kg)(1\cdot 10^{-10} m)^2}=2.4\cdot 10^{-17} J[/tex]

(b) Approximately 10 times larger

The ground state energy of the hydrogen atom is

[tex]E_0 = 13.6 eV[/tex]

Converting into Joules,

[tex]E_0 =(13.6 eV)(1.6\cdot 10^{-19} J/eV)=2.2\cdot 10^{-18}J[/tex]

The kinetic energy of the electron in the previous part of the problem was

[tex]E=2.4\cdot 10^{-17} J[/tex]

So, we see it is approximately 10 times larger.

Final answer:

To determine the kinetic energy of an electron with a de Broglie wavelength equal to the diameter of a hydrogen atom, we use the de Broglie relation to first calculate the momentum and then find the kinetic energy. Subsequently, this energy can be compared to the ground-state energy of a hydrogen atom.

Explanation:

The student is asking about the properties of an electron with a de Broglie wavelength equal to the diameter of a hydrogen atom in its ground state. This problem can be solved using the de Broglie wavelength formula and the known size of the hydrogen atom. We relate the wavelength (λ) to the momentum (p) of the electron using the de Broglie relation λ = h/p, where h is Planck's constant. The diameter of a hydrogen atom in its ground state is approximately the size of the first Bohr orbit, which is about 0.053 nm or 5.3 x 10-11 m.

To find the kinetic energy (KE), we can first calculate the momentum using p = h/λ. Then, KE can be found using the expression KE = p2/2m, where m is the mass of the electron. We thus find the kinetic energy associated with an electron having a wavelength of 5.3 x 10-11 m.

Once the electron's kinetic energy is calculated, we can compare it to the ground-state energy of a hydrogen atom. The ground-state energy of a hydrogen atom is approximately -13.6 eV, where the negative sign indicates that the electron is bound to the nucleus. The kinetic energy of the electron, in this case, will be positive since it represents the energy associated with its motion.

Answer:

they all have the gravity.

Answer:

I believe they all have solid rocky surfaces. Hope this helps and good luck!

Explanation:

Answer:

1 ms⁻¹ .

Explanation:

Speed is defined as the product of the wavelength times the frequency.

If v is the speed , λ is the given wavelength 0.2 m and frequency f is equal to 5 Hertz or wavelengths per second ,

v = λ f = 0.2 x 5 = 1 m/s

Answer:

Connect C₁ to C₃ in parallel; then connect C₂ to C₁ and C₂ in series. The voltage drop across C₁ the 2.0-μF capacitor will be approximately 2.76 volts.

[tex]-1.5\;\mu\text{F}-[\begin{array}{c}-{\bf 2.0\;\mu\text{F}}-\\-3.0\;\mu\text{F}-\end{array}]-[/tex].

Explanation:

Consider four possible cases.

[tex]-\begin{array}{c}-{\bf 2.0\;\mu\text{F}-}\\-1.5\;\mu\text{F}- \\-3.0\;\mu\text{F}-\end{array}-[/tex]

In case all three capacitors are connected in parallel, the [tex]2.0\;\mu\text{F}[/tex] capacitor will be connected directed to the battery. The voltage drop will be at its maximum: 12 volts.

[tex]-3.0\;\mu\text{F}-[\begin{array}{c}-{\bf 2.0\;\mu\text{F}}-\\-1.5\;\mu\text{F}-\end{array}]-[/tex]

In case the [tex]2.0\;\mu\text{F}[/tex] capacitor is connected in parallel with the [tex]1.5\;\mu\text{F}[/tex] capacitor, and the two capacitors in parallel is connected to the [tex]3.0\;\mu\text{F}[/tex] capacitor in series.

The effective capacitance of two capacitors in parallel is the sum of their capacitance: 2.0 + 1.5 = 3.5 μF.

The reciprocal of the effective capacitance of two capacitors in series is the sum of the reciprocals of the capacitances. In other words, for the three capacitors combined,

[tex]\displaystyle C(\text{Effective}) = \frac{1}{\dfrac{1}{C_3}+ \dfrac{1}{C_1+C_2}} = \frac{1}{\dfrac{1}{3.0}+\dfrac{1}{2.0+1.5}} = 1.62\;\mu\text{F}[/tex].

What will be the voltage across the 2.0 μF capacitor?

The charge stored in two capacitors in series is the same as the charge in each capacitor.

[tex]Q = C(\text{Effective}) \cdot V = 1.62\;\mu\text{F}\times 12\;\text{V} = 19.4\;\mu\text{C}[/tex].

Voltage is the same across two capacitors in parallel.As a result,

[tex]\displaystyle V_1 = V_2 = \frac{Q}{C_1+C_2} = \frac{19.4\;\mu\text{C}}{3.5\;\mu\text{F}} = 5.54\;\text{V}[/tex].

[tex]-1.5\;\mu\text{F}-[\begin{array}{c}-{\bf 2.0\;\mu\text{F}}-\\-3.0\;\mu\text{F}-\end{array}]-[/tex].

Similarly,

Charge stored:

[tex]Q = C(\text{Effective}) \cdot V = 1.15\;\mu\text{F}\times 12\;\text{V} = 13.8\;\mu\text{C}[/tex].

Voltage:

[tex]\displaystyle V_1 = V_3 = \frac{Q}{C_1+C_3} = \frac{13.8\;\mu\text{C}}{5.0\;\mu\text{F}} = 2.76\;\text{V}[/tex].

[tex]-2.0\;\mu\text{F}-1.5\;\mu\text{F}-3.0\;\mu\text{F}-[/tex].

Connect all three capacitors in series.

[tex]\displaystyle C(\text{Effective}) = \frac{1}{\dfrac{1}{C_1} + \dfrac{1}{C_2}+\dfrac{1}{C_3}} =\frac{1}{\dfrac{1}{2.0} + \dfrac{1}{1.5}+\dfrac{1}{3.0}} =0.667\;\mu\text{F}[/tex].

For each of the three capacitors:

[tex]Q = C(\text{Effective})\cdot V = 0.667\;\mu\text{F} \times 12\;\text{V} = 8.00\;\mu\text{C}[/tex].

For the [tex]2.0\;\mu\text{F}[/tex] capacitor:

[tex]\displaystyle V_1=\frac{Q}{C_1} = \frac{8.00\;\mu\text{C}}{2.0\;\mu\text{F}} = 4.0\;\text{V}[/tex].

To minimize the voltage drop across the 2.0-μF capacitor, connect it in series with a parallel combination of the 1.5-μF and 3.0-μF capacitors.

To ensure the minimum voltage drop across the 2.0-μF capacitor (C1), we need to arrange the capacitors in such a way that the voltage across C1 is minimized.
The most effective way is to connect C1 in series with a parallel combination of C2 and C3.

Combine C2 and C3 in parallel:

The equivalent capacitance for capacitors in parallel is the sum of their capacitances.

Thus,

Connect Cp in series with C1:

For capacitors in series, the reciprocal of the total capacitance (Ct) is the sum of the reciprocals of the individual capacitances:

Solve for Ct:

Find the voltage drop across C1:

Using the total voltage (Vt) across the capacitors, Vt = 12V, and the voltage division rule for series capacitors, the voltage drop across C1 (V1) can be calculated as:

Substitute the values:

Hence, with this arrangement, the voltage drop across the 2.0-μF capacitor is minimized to approximately 8V.

Answer:

Explanation:

Person A's velocity relative to the train is 0.  Therefore, the pitch of the horn will not change.

Answer:

D. The pitch does not change.

Explanation:

When the source of sound moves away, the pitch drops. and when the source of sound approaches the pitch rises. This is called'Doppler effect'.

Here the person a and the sound horn are both in the same vehicle. Which means their relative velocity is zero. So the horn is neither approaching nor receding the person A

If  the source is approaching

[tex]f_{new}= \frac{v_{sound} }{v_{sound} -v_{source} }f_{original}[/tex]

If the source is receding

[tex]f_{new}= \frac{v_{sound} }{v_{sound} +v_{source} }f_{original}[/tex]

Hence the right answer is option D. The pitch does not change

22.4 L is the answer

hope this help

Answer:

1020 m/s

Explanation:

The moon is in the earth's orbit, meaning it is in free fall.  Its centripetal acceleration is equal to the acceleration due to gravity.

v² / r = GM / r²

v² = GM / r

v = √(GM / r)

G is the universal gravitational constant, M is the mass of the earth, and r is the distance from the earth's center to the moon's center.

G = 6.67×10⁻¹¹ m³/kg/s²

M = 5.97×10²⁴ kg

r = 3.84×10⁸ m

v = √( (6.67×10⁻¹¹) (5.97×10²⁴) / (3.84×10⁸) )

v = 1020 m/s

Answer:

Buzz Aldrin

Explanation:

       Answer:

Buzz Aldrin

       Explanation:

Neil Armstrong was the first man to walk on the moon, but Buzz Aldrin was the second man to walk on the moon. They both walked on the moon on the Apollo 11 Space Mission. Buzz Aldrin was a lunar module pilot working for NASA, and he went up with Neil Armstrong to land on the moon.

Mordancy.

According to Einstein's theory of relativity, a black hole is a "singularity" that consists of a region of the space in which the density of matter tends to infinity. In consequence, this huge massive body has a gravitational pull so strong that not even light can escape from it.  

In addition, "the surface" of a black hole is called the event horizon, which is the border of space-time in which the events on one side of it can not affect an observer on the other side.  

In other words, at this border also called "point of no return", nothing can escape (not even light) and no event that occurs within it can be seen from outside.  

In this sense, and according to the relativity, it is possible to determine where a black hole is if it is "observed" an enormous amount of energy released. So, in accordance to this, galaxies like ours must have a black hole in its center.  

On the other hand, the elliptical galaxy Mesier 87 (also called Virgo A, but from now on M87) was showing the above described behaviour, with enormous jets of high-energy particles shooting away from its vicinity . This was imaged by the Hubble Space Telescope years ago; that is why astronemers were hypothesizing about the existence of a massive black hole there.  

Well now, on April, 10th 2019 this was demonstrated with the publication of the image, for the first time, of the event horizon of the black hole in M87. This is the first time in human history a picture of a black hole is taken.  

This was done by the huge effort of diverse scientist and by the syncronization of eight radio telescopes scattered across the Earth (located at: Hawaii, Spain, Chile, Mexico, Arizona and the South Pole), which took the same point of the sky at the same time.

Answer:

Speed

Explanation:

Speed is a scalar quantity, defined as the ratio between the distance covered and the time taken:

[tex]v=\frac{d}{t}[/tex]

where

d is the distance covered

t is the time taken

Speed is measured in meters/second (m/s).

It should be noted that speed is different from velocity: in fact, velocity is a vector quantity, whose magnitude is defined as

[tex]v=\frac{d}{t}[/tex]

where d is the displacement (not the distance), and it also has a direction, while speed does not have it.

Answer:

Speed

Explanation:

did it on edge 2020

Answer:

Transverse

Explanation:

There are two types of waves, depending on the direction of their oscillations:

- Transverse wave: in a transverse wave, the oscillation occurs in a direction perpendicular to the direction of propagation of the wave. Examples are electromagnetic waves

- Longitudinal wave: in a longitudinal wave, the oscillation occurs parallel to the direction of propagation of the wave. Examples are sound waves

Light waves are just the visible part of the electromagnetic spectrum, therefore they are electromagnetic waves, which consist of oscillations of electric and magnetic field in a direction perpendicular to the direction of propagation of the wave. Therefore, light waves are transverse waves.

Answer: [tex]2.13(10)^{-19} J[/tex]

Explanation:

The photoelectric effect consists of the emission of electrons (electric current) that occurs when light falls on a metal surface under certain conditions.  

If the light is a stream of photons and each of them has energy, this energy is able to pull an electron out of the crystalline lattice of the metal and communicate, in addition, a kinetic energy.  

This is what Einstein proposed:  

Light behaves like a stream of particles called photons with an energy  [tex]E[/tex]

[tex]E=h.f[/tex] (1)

Where:

[tex]h=6.63(10)^{-34}J.s[/tex] is the Planck constant  

[tex]f[/tex] is the frequency

Now, the frequency has an inverse relation with the wavelength [tex]\lambda[/tex]:  

[tex]f=\frac{c}{\lambda}[/tex] (2)  

Where [tex]c=3(10)^{8}m/s[/tex] is the speed of light in vacuum  and [tex]\lambda=400nm=400(10)^{-9}m[/tex] is the wavelength of the absorbed photons in the photoelectric effect.

Substituting (2) in (1):

[tex]E=\frac{h.c}{\lambda}[/tex] (3)

So, the energy [tex]E[/tex] of the incident photon must be equal to the sum of the Work function [tex]\Phi[/tex] of the metal and the maximum kinetic energy [tex]K_{max}[/tex] of the photoelectron:  

[tex]E=\Phi+K_{max}[/tex] (4)  

Rewriting to find [tex]K_{max}[/tex]:

[tex]K_{max}=E-\Phi[/tex] (5)

Where [tex]\Phi[/tex] is the minimum amount of energy required to induce the photoemission of electrons from the surface of a metal, and its value depends on the metal:

[tex]\Phi=h.f_{o}=\frac{h.c}{\lambda_{o}}[/tex] (6)

Being [tex]\lambda_{o}=700nm=700(10)^{-9}m[/tex] the threshold wavelength (the minimum wavelength needed to initiate the photoelectric effect)

Substituting (3) and (6) in (5):  

[tex]K_{max}=\frac{h.c}{\lambda}-\frac{h.c}{\lambda_{o}}[/tex]

[tex]K_{max}=h.c(\frac{1}{\lambda}-\frac{1}{\lambda_{o}})[/tex] (7)

Substituting the known values:

[tex]K_{max}=(6.63(10)^{-34}J.s)(3(10)^{8}m/s)(\frac{1}{400(10)^{-9}m}-\frac{1}{700(10)^{-9}m})[/tex]

[tex]K_{max}=2.13(10)^{-19} J[/tex] >>>>>This is the maximum kinetic energy that ejected electrons must have when violet light illuminates the material

There are "local tsunamis", which are formed near the epicenter of the earthquake and it takes only a few minutes to reach the coast and there are tsunamis whose epicenter is distant (due to an earthquake far away from the place) and it can take up to 22 hours to reach the coastal areas.

For example, in the earthquake ocurred in Japan in 2011, there were areas that were farther from the place where the tsunami was generated, so the inhabitants had between 15 and 20 minutes to evacuate, however, in other places the wave took only 10 minutes on landfall and the inhabitants had only 3 minutes to evacuate.

The difference between the two frequencies used in the operation of a cell phone is [tex]\( 1.224 \times 10^9 \) Hz.[/tex]

To calculate the difference between the frequencies, we first need to find the frequencies of the waves emitted by the base unit and the phone. We can use the formula [tex]\( v = f \times \lambda \)[/tex] , where [tex]\( v \)[/tex]  is the speed of light, [tex]\( f \)[/tex] is the frequency, and [tex]\( \lambda \)[/tex]  is the wavelength.

Given:

Speed of light, [tex]\( v = 2.9979 \times 10^8 \)[/tex] m/s

Wavelength of base unit, [tex]\( \lambda_{base} = 0.34394 \) m[/tex]

Wavelength of phone, [tex]\( \lambda_{phone} = 0.36140 \) m[/tex]

First, let's find the frequency of the wave emitted by the base unit:

[tex]\[ f_{base} = \frac{v}{\lambda_{base}} = \frac{2.9979 \times 10^8}{0.34394} \]\[ f_{base} = 8.720 \times 10^8 \text{ Hz} \][/tex]

Next, let's find the frequency of the wave emitted by the phone:

[tex]\[ f_{phone} = \frac{v}{\lambda_{phone}} = \frac{2.9979 \times 10^8}{0.36140} \]\[ f_{phone} = 8.288 \times 10^8 \text{ Hz} \][/tex]

Now, we can find the difference between the frequencies:

[tex]\[ \Delta f = |f_{base} - f_{phone}| = |8.720 \times 10^8 - 8.288 \times 10^8| \]\[ \Delta f = 1.224 \times 10^8 \text{ Hz} \][/tex]

So, the difference between the two frequencies used in the operation of a cell phone is [tex]\( 1.224 \times 10^8 \) Hz, or \( 122.4 \text{ MHz} \).[/tex]

Complete Question:
Two radio waves are used in the operation of a cellular telephone. To receive a call, the phone detects the wave emitted at one frequency by the transmitting station or base unit. To send your message to the base unit, your phone emits its own wave at a different frequency. The difference between these two frequencies is fixed for all channels of cell phone operation. Suppose the wavelength of the wave emitted by the base unit is 0.34394 m and the wavelength of the wave emitted by the phone is 0.36140 m. Using a value of 2.9979 108 m/s for the speed of light, determine the difference between the two frequencies used in the operation of a cell phone.

The frequency difference between the waves emitted by the base unit and the phone is calculated by determining each frequency and subtracting them. The resulting difference is 42.1 MHz.

Calculating the Frequency Difference for Cellular Phone Signals

To determine the difference in frequencies between the wave emitted by the base unit and the wave emitted by the phone, we use the relationship c = fλ, where c is the speed of light (2.9979 × 108 m/s), f is the frequency, and λ is the wavelength.

Step-by-Step Calculation

Step 1: Calculate the frequency of the wave emitted by the base unit.

[tex]f_{base} = c / \lambda_{base}\\f_{base} = 2.9979 × 10^8 m/s / 0.34394 = 8.714 \times 10^8 Hz[/tex]

Step 2: Calculate the frequency of the wave emitted by the phone.

[tex]f_{phone} = c / \lambda _{phone} \\f_{phone} = 2.9979 \times 10^8 m/s / 0.36140 = 8.293 \times 10^8 Hz[/tex]

Step 3: Find the difference between the two frequencies.

[tex]\Delta f = f_{base} - f_{phone} \\\Delta f = (8.714 \times 10^8 Hz) - (8.293 \times 10^8 Hz)\Delta f = 4.21 \times 10^7 Hz[/tex]

The difference between the two frequencies used in the operation of the cell phone is [tex]4.21 \times 10^7 Hz[/tex] or 42.1 MHz.