electromagnetic wave, with wavelength 3 m, travels in vacuum in the positive x direction with its electric vector e, of amplitude 252.9 v/m, directed along y axis. what is the frequency f of the wave?

To solve this problem, we can use the equations related to the reflection and transmission of electromagnetic waves at the interface between two media. Here are the steps to determine the values:

(a) Γ (reflection coefficient):

The reflection coefficient is given by the formula:

Where Z1 and Z2 are the impedance of the first and second media, respectively. In this case, Z1 = Z0 (impedance of free space) and Z2 = Z0 / √εr (impedance of the dielectric medium).

Using εr = 36, we can calculate Z2 as follows:

Now, substitute the values into the reflection coefficient equation:

(b) Average power densities:

The average power density of the incident wave is given by:

where ε0 is the permittivity of free space and c is the speed of light.

Substituting the given values:

The average power density of the reflected wave is the same as the incident wave, as there is no absorption in the perfect dielectric medium.

(c) Distance to the nearest minimum of |E|:

For a normally incident wave on a dielectric interface, the electric field intensity follows a sinusoidal variation as a function of distance from the boundary. The distance to the nearest minimum of |E| can be calculated using the wavelength of the wave in the medium.

The wavelength in the dielectric medium is given by:

where λ0 is the wavelength in free space and εr is the relative permittivity of the dielectric medium.

Using εr = 36 and the frequency of 50 MHz, we can calculate λ as follows:

Since the wave is normally incident, the distance to the nearest minimum of |E| is half the wavelength, i.e., 3 m.

So, the answers are:

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The specific gravity of the other fluid is 2.43, When filled with another fluid, the mass is 88.78g.

The specific gravity of a substance is the ratio of its density to the density of water. In this case, we can use the masses of the empty bottle, the bottle filled with water, and the bottle filled with the other fluid to calculate the specific gravity of the other fluid.
First, we need to calculate the mass of the water in the bottle, which is the difference between the mass of the filled bottle and the mass of the empty bottle:
mass of water = 98.44g - 35.0g = 63.44g
Next, we can use the mass of the water and the density of water (1.00 g/mL) to calculate the volume of the water:
volume of water = mass of water / density of water = 63.44g / 1.00 g/mL = 63.44 mL
Now, we can use the mass of the bottle filled with the other fluid and the volume of the water to calculate the density of the other fluid:
mass of other fluid = 88.78g
volume of other fluid = volume of bottle - volume of water = 100mL - 63.44mL = 36.56 mL
density of other fluid = mass of other fluid / volume of other fluid = 88.78g / 36.56 mL = 2.43 g/mL
Finally, we can calculate the specific gravity of the other fluid by dividing its density by the density of water:
specific gravity = density of other fluid / density of water = 2.43 g/mL / 1.00 g/mL = 2.43
Therefore, the specific gravity of the other fluid is 2.43.

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If we treat an electron as a classical rigid sphere with a radius of 1.20×10−17 mm and uniform density, we can use the formula for the moment of inertia of a solid sphere: I = (2/5)mr^2, where m is the mass of the electron and r is the radius of the sphere. The mass of an electron is 9.11×10^-31 kg.

So, I = (2/5)(9.11×10^-31 kg)(1.20×10−17 mm)^2 = 1.03×10^-52 kg·m^2

If we assume that the electron is rotating around its own axis, we can use the formula for rotational kinetic energy: K = (1/2)Iω^2, where ω is the angular speed.

Assuming that the electron is not interacting with any external forces, the total energy of the system is conserved. Therefore, we can equate the rotational kinetic energy to the rest energy of the electron (given by Einstein's famous formula E = mc^2), which is 8.19×10^-14 J.

So, (1/2)Iω^2 = 8.19×10^-14 J

ω^2 = (2/5)(8.19×10^-14 J)/(1.03×10^-52 kg·m^2) = 1.28×10^38 s^-2

ω = √(1.28×10^38 s^-2) = 1.13×10^19 s^-1

Therefore, the angular speed of the electron treated as a classical rigid sphere with uniform density and radius 1.20×10−17 mm is approximately 1.13×10^19 s^-1.

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Answer:

The amplitude of a sound wave decreases with distance from its source, because the energy of the wave is spread over a larger and larger area.

Explanation:

A larger amplitude means a louder sound, and a smaller amplitude means a softer sound.

Answer: Amplitude of sound

Explanation: The amplitude of sound decreases as we get further away from the source of a sound.

Amplitude is a measure of the size of sound waves. It depends on the amount of energy that started the waves. Greater amplitude waves have more energy and greater intensity, so they sound louder.

As the distance from the sound source increases, the area covered by the sound waves increases. The same amount of energy is spread over a greater area, so the intensity and loudness of the sound are less. This explains why even loud sounds fade away as you move farther from the source.

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To calculate the power wasted when electricity is delivered at different voltages, we can use the formula:

Power wasted = (I^2) * R

Where:

I is the current flowing through the wires

R is the total resistance of the wires

First, let's calculate the current flowing through the wires using Ohm's Law:

I = V / R

Where:

V is the voltage

For the first case, where the electricity is delivered at 50,000 V:

I = 50,000 V / 3.0 Ω

Calculating the current:

I ≈ 16,667 A

Now, we can calculate the power wasted using the formula:

Power wasted = (I^2) * R

Power wasted = (16,667 A)^2 * 3.0 Ω

Power wasted ≈ 0.835 MW

Now, let's calculate the power wasted when the electricity is delivered at 12,000 V:

I = 12,000 V / 3.0 Ω

Calculating the current:

I ≈ 4,000 A

Power wasted = (4,000 A)^2 * 3.0 Ω

Power wasted ≈ 48 MW

To calculate the difference in power wasted, we subtract the power wasted at 50,000 V from the power wasted at 12,000 V:

Difference in power wasted = Power wasted (12,000 V) - Power wasted (50,000 V)

Difference in power wasted ≈ 48 MW - 0.835 MW

Difference in power wasted ≈ 47.165 MW

Therefore, if the electricity is delivered at 50,000 V instead of 12,000 V, approximately 47.165 MW less power is wasted.

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The author advises to make sure the red and black cables are connected to the corresponding terminals, and to connect the red cable to the dead battery first.

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The amount of energy required to convert all the ice and water into steam is 12,955,520 J.

To convert all the ice and water into steam, we need to calculate the amount of energy required for each step of the process. First, we need to calculate the energy required to raise the temperature of the ice from -9 °C to 0 °C using the specific heat capacity of ice.

Then, we need to calculate the energy required to melt the ice at 0 °C using the latent heat of fusion of ice. Next, we need to calculate the energy required to raise the temperature of the resulting water from 0 °C to 21 °C using the specific heat capacity of water.

After that, we need to calculate the energy required to raise the temperature of the water from 21 °C to 100 °C and then to convert it into steam at 100 °C using the specific heat capacity of water and the latent heat of vaporization of water.

When all these energies are added together, we get the total amount of energy required, which is 12,955,520 J.

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As n increases without bound, the energy of the electron does not increase without bound but approaches a finite value known as the ionization energy.

As the principal quantum number n increases without bound, the energy of the electron in a hydrogen atom approaches a finite value known as the ionization energy, which is the energy required to completely remove the electron from the hydrogen atom.

The ionization energy for hydrogen is approximately 13.6 eV (electron volts). Once the electron is removed, the remaining system has zero energy, as the electron was the only constituent that had energy. Therefore, the energy of the electron in a hydrogen atom does not increase without bound, but rather approaches a finite value of the ionization energy as n increases.

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The I & O Psychology researchers are most interested in areas such as personnel selection, job analysis, performance management, organizational development etc..

The personnel selection is a critical area that involves developing methods to identify the most qualified candidates for job positions. This area encompasses techniques such as job analysis, interview strategies and personality assessments.

Another area is performance management which involves developing effective performance appraisal systems, feedback mechanisms and coaching strategies to enhance employee performance. These are examples of diverse areas of interest within Industrial and Organizational Psychology.

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Answer:

High

Explanation:

Waves with high energy have a higher frequency.

A motor with a horsepower rating of approximately 56.4 hp is required to drive the pump, assuming a pump efficiency of 70%.

To calculate the horsepower rating of the motor needed to power the pump, the following formula can be used:

Power = (Flow rate x Head x Density) / (Efficiency x 3960)

where:

Power is the required power in horsepower (hp).

Flow rate is the volumetric flow rate of water in gallons per minute (gpm).

Head is the total dynamic head of the pump in meters (m).

Density is the density of water in pounds per gallon (lb/gal).

Efficiency is the pump efficiency expressed as a decimal (e.g., 70% = 0.7).

3960 is a conversion factor to convert units to horsepower (hp).

The flow rate needs to be converted from gallons per minute to cubic meters per second by dividing by 15850.4, which is the conversion factor for the two units. Therefore:

Flow rate = 150 gpm / 15850.4 gpm/m^3 = 0.00946 m^3/s

The head needs to be converted from meters to feet to match the units used in the formula. This can be done by multiplying the head by 3.281. Hence:

Head = 120 m x 3.281 ft/m = 393.7 ft

The density of water also needs to be converted from pounds per gallon to kilograms per cubic meter to match the flow rate units. This can be accomplished by using the conversion factor of 0.45359 kg/lb. Therefore:

Density = 8.34 lb/gal x 0.45359 kg/lb / 0.00378541 m^3/gal = 999.1 kg/m^3

Substituting these values into the formula, we get:

Power = (0.00946 m^3/s x 393.7 ft x 999.1 kg/m^3) / (0.7 x 3960) = 56.4 hp

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Answer:

Zhaozhou Bridge was built in the Sui Dynasty between 595 and 605. It has a history of more than 1,400 years. It is the crystallization of the wisdom of the ancient working people and has opened a new situation in bridge construction in China.

Zhaozhou Bridge is the oldest, longest span and best preserved single-aperture open-shoulder stone arch bridge in the world. In 2015, it was awarded as one of the top ten City Business Cards of Shijiazhuang. Zhaozhou Bridge is a single span stone arch bridge, its design is both beautiful and scientific. The structure of the whole bridge is well-proportioned and harmonized with the surrounding scenery. The stone balustrades on the bridge are beautifully carved. The high technical level and immortal artistic value of Zhaozhou Bridge fully demonstrate the wisdom and strength of the Chinese working people. Zhaozhou Bridge is second to none among ancient Bridges in China. According to bridge studies in countries around the world, open-shouldered arch Bridges like these did not appear in Europe until the mid-19th century, more than 1,200 years later than our own. After the completion of Zhaozhou Bridge, the initial name is Zhaojun River Stone Bridge. It was named after the place name and water name of the time, and it was here that the original name began. Zhaozhou Dashi Bridge is the common name of local people. Yongtong Bridge was built on the Ye River (Qingshui River) outside the west gate of Zhaozhou City, later than Zhaojun River Stone Bridge, with similar architectural structure and artistic style, but smaller shape. It is only 2.5 kilometers away from Zhaojun River Stone Bridge, so it is called Zhaozhou Dashi Bridge because its size can distinguish the second north-south bridge. Zhaozhou Bridge is named after a place name. Since the northern Qi Tianbao two years, Yanzhou changed to Zhaozhou, Zhaozhou name from this.

The distance of the image is around -9.08 cm, indicating that it is a virtual image formed on the same side as the object. The size of the image is roughly 0.256 times the size of the object.

To determine the image distance and image size formed by a diverging lens, we can use the lens formula and magnification formula. The lens formula is given by:

1/f = 1/v - 1/u

where f is the focal length of the lens, v is the image distance, and u is the object distance.

Given:

Object distance (u) = -35.5 cm (negative sign indicates a virtual object)

Focal length (f) = -12.2 cm (negative sign indicates a diverging lens)

Using the lens formula, we can solve for the image distance (v):

1/(-12.2) = 1/v - 1/(-35.5)

Simplifying the equation, we get:

-0.08197 = 1/v + 0.02817

Rearranging the terms, we have:

1/v = -0.08197 - 0.02817

1/v = -0.11014

Taking the reciprocal of both sides, we find:

v = -9.08 cm

The negative sign indicates that the image is formed on the same side as the object, indicating a virtual image.

To calculate the image size, we can use the magnification formula:

magnification (m) = -v/u

Substituting the values, we get:

m = -(-9.08) / (-35.5)

m ≈ 0.256

The negative sign in the magnification indicates that the image is upright.

The image distance is approximately -9.08 cm (virtual image formed on the same side as the object), and the image size is approximately 0.256 times the size of the object.

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The range of electromagnetic radiation emitted when transitions from higher levels into n = 1 occur in a hydrogen atom includes ultraviolet, visible, and infrared radiation.

When transitions from higher energy levels to the n = 1 energy level occur in a hydrogen atom, a range of electromagnetic radiation is emitted. This emission includes ultraviolet, visible, and infrared radiation.

The specific wavelength or frequency of the emitted radiation depends on the energy difference between the initial and final energy levels of the transition. Transitions from higher energy levels to the n = 1 energy level correspond to higher energy differences, resulting in the emission of shorter wavelength ultraviolet radiation.

As the energy differences decrease, the emitted radiation shifts towards longer wavelengths, covering the visible spectrum and extending into the infrared region.

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The magnetic flux passing through defined by 0.02 < r < 0.03 m and 0 < z < 3 is `8π × 10⁻⁷ Wb`

Permeability of free space is given by `μ0 = 4π × 10⁻⁷ T m A⁻¹`

Formula used to calculate the magnetic flux passing through the defined area is as follows:

`ΦB = μ0 * I * (Θ2 - Θ1) / 4π`

Where

I = current

Θ1 = lower limit of angle

Θ2 = upper limit of angle

For the given problem, current filament is along the z – axis in the direction, thus the angle Θ1 and Θ2 will be 0 and 2π respectively.

The distance between 0.02 m and 0.03 m is 0.01 m, the mean radius of the area will be`(0.03 + 0.02) / 2 = 0.025 m`

The formula for calculating the magnetic flux through the defined area is`ΦB = μ0 * I * (Θ2 - Θ1) / 4π`

From the question, we know that;:

μ0 = `4π × 10⁻⁷ T m A⁻¹`

I = 4A

Θ1 = 0

Θ2 = 2π

The formula becomes`ΦB = (4π × 10⁻⁷) * 4 * (2π - 0) / 4π``ΦB = 8π × 10⁻⁷ Wb`

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The tension in the string is equal to the weight of the cylinder minus the buoyant force acting on it. Therefore, the tension in the string is 34.29 N.

The weight of the cylinder is given by the formula:

w = mg

where m is the mass of the cylinder and g is the acceleration due to gravity.

w = 4.0 kg x 9.81 m/s^2 = 39.24 N

The volume of the cylinder is given by the formula:

V = m / ρ

where ρ is the density of iron.

V = 4.0 kg / 7860 kg/m^3 = 5.08 x 10^-4 m^3

The buoyant force is given by the formula:

F_b = ρ_w V g

where ρ_w is the density of water and g is the acceleration due to gravity.

F_b = 1000 kg/m^3 x 5.08 x 10^-4 m^3 x 9.81 m/s^2 = 4.95 N

Therefore, the tension in the string is:

T = w - F_b = 39.24 N - 4.95 N = 34.29 N.

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The maximum height reached by the projectile is approximately 283.13 meters.

To determine the velocity of the projectile 2 seconds after firing, we need to break down the initial velocity into its horizontal and vertical components.

The horizontal component remains constant throughout the motion, so it will be the same as the initial velocity: 150 m/s.

For the vertical component, we can use the equation v = u + at, where v is the final velocity, u is the initial vertical velocity component, a is the acceleration due to gravity (-9.8 m/s^2), and t is the time.

Since the projectile is fired upwards, the initial vertical velocity component is given by u = u_initial * sin(angle), where u_initial is the initial velocity (150 m/s) and the angle is 47 degrees.

Using this information, we can calculate the vertical velocity component at t = 2 seconds:

v = u + at

v = (u_initial * sin(angle)) + (a * t)

v = (150 * sin(47)) + (-9.8 * 2)

v ≈ 76.65 - 19.6

v ≈ 57.05 m/s

So, the velocity of the projectile 2 seconds after firing is approximately 57.05 m/s.

To determine the total time in the air, we need to find when the projectile returns to the same height from which it was launched. The total time in the air can be calculated using the equation t = (v_final - u_initial * sin(angle)) / (-a), where v_final is the final vertical velocity component (0 m/s).

0 = (u_initial * sin(angle)) + (-9.8 * t_total)

t_total = (u_initial * sin(angle)) / 9.8

Using the given values, the total time in the air is approximately:

t_total = (150 * sin(47)) / 9.8

t_total ≈ 6.42 seconds

So, the total time in the air is approximately 6.42 seconds.

To determine the maximum height reached by the projectile, we can use the equation h_max = (u_initial^2 * sin^2(angle)) / (2 * a), where h_max is the maximum height.

h_max = (150^2 * sin^2(47)) / (2 * 9.8)

h_max ≈ 283.13 meters

Therefore, the maximum height reached by the projectile is approximately 283.13 meters.

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The frequency of the photon absorbed when the hydrogen atom makes the transition from the ground state to the n=4 state is 2.47 x 10^14 Hz.

The energy of a photon emitted or absorbed in the hydrogen atom transition is given by the formula

E = hf, where E is the energy of the photon, h is Planck's constant, and f is the frequency of the photon.

The energy difference between the n=4 state and the ground state of hydrogen is ΔE = -13.6 eV (1/4^2 - 1/1^2).

Therefore, the energy of the absorbed photon is 13.6 eV.

Converting this to joules and substituting it into the energy formula gives E = hf.

Solving for f, we get f = E/h, which is approximately 2.47 x 10^14 Hz.

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The half-life of the given element is approximately 25.33 years.

In the decay function, a(t) = a * e^(-0.0274t), the parameter λ = 0.0274 is the decay constant of the radioactive element  The half-life of the element is the amount of time it takes for half of the initial amount of the element to decay. We can determine the half-life by setting a(t) = 0.5a in the decay function and solving for t.

This gives us t = ln(2) / λ.

Substituting the value of λ into this equation, we get t = ln(2) / 0.0274 ≈ 25.33 years. Therefore, the half-life of the radioactive element is approximately 25.33 years.

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No, energy is not destroyed when the vibrations of incident and reflected waves cancel at the nodes in a standing wave.

In a standing wave, the incident and reflected waves interfere with each other, creating a pattern of nodes (points of no displacement) and antinodes (points of maximum displacement).

At the nodes, the waves cancel each other out due to destructive interference, but this does not mean that energy is destroyed.

Instead, the energy is redistributed in the form of constructive interference at the antinodes, where the incident and reflected waves add together.

This redistribution of energy maintains the overall energy within the system, in accordance with the law of conservation of energy.
Although the vibrations of incident and reflected waves cancel at the nodes in a standing wave, energy is not destroyed. The energy is redistributed and conserved within the system, manifesting as constructive interference at the antinodes.

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If the tube diameter and length both double while everything else remains the same, the Reynolds number, which is the dimensionless quantity that characterizes the flow regime, remains the same because the fluid velocity, viscosity, and density remain constant. Therefore, the flow remains laminar.

The volume flow rate (Q) in laminar flow is given by:

Q = (π/8) * (d^4) * ΔP / μL

where d is the tube diameter, ΔP is the pressure difference between the ends of the tube, μ is the fluid viscosity, and L is the tube length.

If both d and L double, we have:

Q' = (π/8) * (2d)^4 * ΔP / μ(2L)

Q' = 16 * (π/8) * d^4 * ΔP / μL

Q' = 2 * Q

Therefore, the volume flow rate increases by a factor of 2.

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The impulse experienced by the catcher when catching the baseball can be calculated using the impulse-momentum principle, which states that the impulse is equal to the change in momentum of the object.

The impulse is given by:
Impulse = Change in momentum
The momentum of an object is given by the product of its mass and velocity. In this case, the mass of the baseball is 145 g, which is equal to 0.145 kg, and its velocity is 38.0 m/s. Therefore, the initial momentum of the baseball is:
Initial momentum = mass * initial velocity = 0.145 kg * 38.0 m/s
Assuming the catcher catches the ball and brings it to rest, the final momentum of the baseball is zero since its velocity becomes zero. Hence, the change in momentum is:
Change in momentum = Final momentum - Initial momentum
Change in momentum = 0 - (0.145 kg * 38.0 m/s)
The impulse experienced by the catcher is equal to the change in momentum, so:
Impulse = -0.145 kg * 38.0 m/s
The average force exerted on the catcher by the baseball can be calculated using the equation:
Force = Impulse / Time
We have already calculated the impulse, which is -0.145 kg * 38.0 m/s. The time taken for the ball to stop once in contact with the catcher's glove is given as 23.0 ms, which is equal to 0.023 s. Substituting the values into the equation, we can calculate the average force:
Force = (-0.145 kg * 38.0 m/s) / 0.023 s
Therefore, the average force exerted by the ball on the catcher is equal to the calculated value.

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Answer:

I hope this helps ^^

Explanation:

If more factories start using large tanks of bacteria to remove carbon dioxide from the atmosphere, it would likely lead to a decrease in the overall amount of carbon dioxide in the atmosphere. Carbon dioxide is a greenhouse gas that contributes to the greenhouse effect, trapping heat in the Earth's atmosphere and causing global warming.

With a decrease in the amount of carbon dioxide, the total amount of energy in the Earth system would be affected. Carbon dioxide acts as a blanket, trapping heat from the sun and preventing it from escaping back into space. When the concentration of carbon dioxide decreases, less heat is trapped, resulting in a reduction of the total energy within the Earth system.

As for the global average temperature, the decrease in carbon dioxide levels would have a cooling effect on the planet. Since carbon dioxide is a major contributor to the greenhouse effect, its reduction would reduce the overall warming impact. This could lead to a decrease in the global average temperature, potentially slowing down or mitigating the rate of global warming.

However, it's important to note that the relationship between carbon dioxide levels, energy balance, and global temperature is complex and influenced by various factors. The impact of reducing carbon dioxide through bacteria tanks would depend on the scale of implementation, the effectiveness of the technology, and other factors that affect the Earth's climate system.

When a hammer strikes a nail, the nail exerts an unbalanced force that changes its velocity.

So, the answer is C.

A force is described as a push or a pull that can cause an object to move or change direction.

When a force acts upon an object, the object is compelled to either stop, accelerate, or change direction. Force can be measured in units of newtons (N).There are two types of forces: balanced and unbalanced forces.

When two forces are equal in magnitude and opposite in direction, they are considered balanced forces. When two forces are unequal in magnitude or direction, they are considered unbalanced forces.

When a hammer strikes a nail, the nail exerts an unbalanced force that changes its velocity. The hammer exerts a force on the nail, driving it into the wood.

Hence, the answer of the question is C.

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The  average diameter of an air molecule is approximately 0.364 nm.

The mean free path of an air molecule, λ, is related to the diameter of the molecule, d, and the number density of molecules, n, by the formula:

λ = 1/(√2πd^2n)

We can rearrange this formula to solve for the diameter of an air molecule:

d = √(1/(2πnλ))

The number density of molecules, n, is equal to the mass density of air divided by the mass of one molecule:

n = ρ / (mu * N_A)

where ρ is the mass density of air, mu is the average molecular mass of air, and N_A is Avogadro's number. Substituting the given values, we get:

n = 1.29 kg/m^3 / (29.0 u * 1.66 × 10^-27 kg/u * 6.02 × 10^23/mol) ≈ 2.46 × 10^25 m^-3

We are given that the mean free path of an air molecule at room temperature is λ = 111 nm = 111 × 10^-9 m. Substituting the values into the formula for the diameter of an air molecule, we get:

d = √(1/(2πnλ)) ≈ 0.364 nm

Therefore, the average diameter of an air molecule is approximately 0.364 nm.

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The required correct answer is A - the type of materials the objects are made of.

The force of friction between two solid objects depends on various factors such as the smoothness of the surfaces in contact, the contact force between the objects, and the relative speed of the objects to each other. The force of friction arises due to the interlocking of surface irregularities between two solid objects in contact, which resists the relative motion between them. The smoother the surfaces, the less force is required to overcome the friction. Similarly, the force of friction increases with the contact force between the objects and the relative speed of the objects to each other. However, the type of materials the objects are made of does not affect the force of friction, as long as they are both solid and in contact. Thus, the force of friction is an important concept in physics, which has numerous applications in daily life.

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The average speed of this object having a graph like this is

10/5 = 2 meter/minute. Because this object changes distance of 10 m in 5 minutes of time. Hence option B is correct.

Speed is a rate of change of distance with respect to time. i.e. v=dx÷dt. Speed can also be defined as distance over time i.e. speed= distance ÷ time it is denoted by v and its SI unit is m/s. it is a scalar quantity. Speed shows how much distance can be traveled in unit time.

To find dimension for speed is, from formula Speed = Distance ÷ Time Dimension for distance is [L¹] , Dimension for Time is [T¹], Dividing dimension of distance by dimension of time gives, [L¹] ÷ [T¹] = [L¹T⁻¹] Dimension for speed is [L¹T⁻¹].

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The half-life of the radioactive substance is 1.8 hours.


The half-life of a radioactive substance is the time it takes for half of the substance to decay. Using the given information, we can calculate the amount of substance left after one half-life:
2.46 g ÷ 2 = 1.23 g
We can see that 0.076875 g is approximately 1/16 of 1.23 g, which means that 4 half-lives have passed:
1 half-life: 2.46 g ÷ 2 = 1.23 g
2 half-lives: 1.23 g ÷ 2 = 0.615 g
3 half-lives: 0.615 g ÷ 2 = 0.308 g
4 half-lives: 0.308 g ÷ 2 = 0.154 g
Since 4 half-lives have passed in 9.5 hours, we can calculate the half-life as:
9.5 h ÷ 4 = 2.375 h per half-life
Rounding to one significant figure, the half-life of the substance is 1.8 hours.

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