Rounded to two significant figures, the initial activity of the sample was approximately 390000 μCi.
We have,
The decay of a radioactive substance follows an exponential decay formula:
N(t) = N₀ [tex](1/2)^{t / T},[/tex]
where:
N(t) is the quantity of the substance remaining at time t.
N₀ is the initial quantity of the substance.
t is the time that has passed.
T is the half-life of the substance.
In this case, we are given:
Half-life (T) = 32.5 days,
Activity after 97.5 days (N(97.5d)) = 3.1 Ci.
Since activity (A) is proportional to the quantity of the substance
(A = λ * N), we can write:
[tex]A(t) = A_0 ~(1/2)^{t / T},[/tex]
where:
A(t) is the activity at time t.
A₀ is the initial activity.
Given that A(97.5d) = 3.1 Ci, we can substitute the values and solve for A₀:
3.1 Ci = A₀ x [tex](1/2)^{97.5d / 32.5d}.[/tex]
Solving for A₀:
[tex]A_0 = 3.1 Ci / (1/2)^{97.5d / 32.5d}\\A_0= 3.1 Ci / (2^{3)}.[/tex]
Calculating:
A₀ ≈ 0.3875 Ci.
Now, we need to convert this to microcuries (μCi):
1 Ci = [tex]10^6[/tex] μCi,
So,
A₀ = 0.3875 Ci x [tex]10^6[/tex] μCi/Ci ≈ 387500 μCi.
Thus,
Rounded to two significant figures, the initial activity of the sample was approximately 390000 μCi.
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The complete question:
The radioactive decay of cesium-141 (Ce-141) has a half-life of 32.5 days. After 97.5 days have elapsed, a sample of Ce-141 has an activity of 3.1 curies (Ci). What was the initial activity, in microcuries (μCi), of the sample? Provide your answer using two significant figures.
To find the initial activity of the sample, we can use the concept of radioactive decay and the given half-life and activity measurements.Rounding to two significant figures, the initial activity of the sample is approximately 2.5 * 10^7 microcuries (μCi).
1. The half-life of cesium-141 (Ce-141) is 32.5 days, which means that every 32.5 days, the activity of the sample is reduced by half.
2. After 97.5 days, the activity of the sample is measured to be 3.1 curies (Ci).
To find the initial activity, we need to determine how many half-lives have occurred in 97.5 days. We can do this by dividing 97.5 days by the half-life of 32.5 days.
3. 97.5 days ÷ 32.5 days = 3 half-lives.
Since each half-life reduces the activity by half, three half-lives will reduce the activity to (1/2) * (1/2) * (1/2) = 1/8 of the initial activity.
4. Therefore, the current activity is 1/8 of the initial activity.
Given that the current activity is 3.1 curies (Ci), we can find the initial activity by multiplying the current activity by 8.
5. 3.1 curies * 8 = 24.8 curies.
To convert the activity to microcuries (μCi), we can multiply by 10^6 since 1 curie is equal to 10^6 microcuries.
6. 24.8 curies * 10^6 = 2.48 * 10^7 microcuries (μCi).
Rounding to two significant figures, the initial activity of the sample is approximately 2.5 * 10^7 microcuries (μCi).
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Which of these statements best describes the difference between electromagnetic and gravitational forces in the solar system?
a. Electromagnetic forces have a shorter range than gravitational forces.
b. Electromagnetic forces are stronger than gravitational forces.
c. Electromagnetic forces are only repulsive but gravitational forces are both attractive and repulsive.
d. Electromagnetic forces are only attractive but gravitational forces are both attractive and repulsive.
Answer:
Electromagnetic forces are stronger than gravitational forces.
Explanation:
Electromagnetic and gravitational forces both are fundamental forces present in nature. The force that exists between the charged particles are electromagnetic forces while the force that exists between two objects in the universe is called gravitational force.
The one of the difference between these two forces is that the gravitational force is always attractive while the electromagnetic force can be attractive or repulsive.
Electromagnetic forces are stronger than gravitational forces. It is approximate 10³⁹ times stronger than gravitational force. Hence, the correct option is (b).
A circuit with a resistance of 25 ohms is carrying a current of 2
a. how much heat, in watts, is developed?
You can find all the naturally occurring compounds on the periodic table. true or false
The police department is very proud of their new police cars. They announced that they are able to go from a stopped position to 80 miles per hour in 6 seconds. They are describing their cars' velocity. direction. speed. acceleration.
You are waiting to turn left into a small parking lot. a car approaching from the opposite direction has a turn signal on. you should _______________.
A double solid white line painted between lanes on the highway means Changing lanes is not allowed. True or false?
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. the total volume of the solid is 2 cubic centimeters. find the radius of the cylinder that produces the minimum surface area. (round your answer to three decimal places.)
To find the radius of the cylinder that produces the minimum surface area, combine the volume equations and isolate for the radius. Then, use calculus to find the minimum point for the surface area. Round the resulting value to three decimal places.
Explanation:The subject of this mathematical problem involves the principles of calculus and geometry. The volume of the entire solid is the sum of the volume of the two hemispheres and the volume of the cylinder. Given that the total volume of the solid is 2 cm³, we know that the volume of the cylinder plus two times the volume of one hemisphere is equal to 2 cm³.
By expressing volume in terms of the radius, we can find that the radius equals the cube root of the volume divided by π (since the volume of a sphere is 4/3πr³ and the volume of a cylinder is πr²h, while considering the height of the cylinder equal to the diameter of the hemisphere). The surface area of the solid is the sum of the surface area of the two hemispheres and the surface area of the cylinder without tops (since those are covered by the hemispheres). To minimize the surface area, we need to use calculus, specifically the principles of differentiation and setting the derivative equal to zero to find a minimum. Once calculated, you can round the radius to three decimal places.
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What measurement can be used to determine the stability of the atmosphere?
Final answer:
The stability of the atmosphere is determined using various measurements such as temperature and pressure data, weather station and satellite observations, and analyses of natural records like tree rings and ice cores.
Explanation:
To determine the stability of the atmosphere, scientists and meteorologists use various measurements. These include temperature and pressure gradients, the analysis of weather station data, and satellite observations. For instance, observations from mountain summits can provide vital data above the main body of our atmosphere, while meteorological observations of meteors can offer insights into the height of Earth's atmosphere. Additionally, indicators like the annual rings in trees and ice core analysis can predict long-term atmospheric changes, such as Earth's temperature trends. CO₂ concentrations measured from ice traps and deuterium analysis also reveal historical climate data, informing about past atmospheric stability. Furthermore, the Gravity Recovery and Climate Experiment (GRACE) by NASA enables scientists to measure mass changes in Earth's water resources which is critical for understanding climatic and atmospheric variations.
Why will many of the very large telescopes of the future make use of multiple mirrors?
Adoptive optics, in which it’s a lot easier for a computer to constantly monitor and change the shape of multiple thin mirrors than it is to use a telescope with a large thick mirror that has to thermally adjust before being able to focus sharply and even then a large mirror or lens cannot compensate for air turbulence the way telescope with computer controlled adaptive optics can.
An important part of developing motivation includes understanding that motivation is influenced by your _____.
the answer is positive mindset : )
If you were asked to describe metals and magnetism you could say
a. non–paired electrons spin in opposite directions in all metals, creating a magnetic field.
b. metals are magnets because they have more electrons than non–magnetic materials.
c. metals can become magnetic if they have many spinning electrons that create magnetic fields.
d. the electrons in some metals pair up to create a magnetic field.
Answer:
d. the electrons in some metals pair up to create a magnetic field.
Explanation:
Magnetism is the property of attraction and repulsion of certain metals and magnets, which have a positive and a negative pole, characterized by “dipole forces”. When magnetism occurs the electrons in some metals come together to create a magnetic field. The Magnetic Field, in turn, is the concentration of magnetism that is created around a magnetic charge in a given space.
It is the electrons of metals that create the magnetic field, just as it is the electric charge and mass that respectively create the electric and gravitational fields.
If a wave has a wavelength of 9 meters and a period of 0.006, what is the velocity of the wave?
Answer : Velocity of the wave, v = 1500 m/s.
Explanation :
It is given that,
Wavelength of a wave, [tex]\lambda=9\ m[/tex]
Time period of wave, [tex]T=0.006\ s[/tex]
We know that the relation between the velocity, the frequency and the wavelength is given by :
[tex]v=\nu\times \lambda[/tex]
[tex]\because\ \nu=\dfrac{1}{T}[/tex]
[tex]v=\dfrac{\lambda}{T}[/tex]
[tex]v=\dfrac{9\ m}{0.006\ s}[/tex]
[tex]v=1500\ m/s[/tex]
Hence, this is the required solution.
What are two different ways to understand time? Explain and give example
Solar time and sidereal time are two different ways to understand time. Solar time is based on the position of the Sun in the sky and changes throughout the day, while sidereal time is based on the rotation of the Earth relative to the stars and remains constant. Examples of solar time include a sundial, while examples of sidereal time include a telescope tracking the motion of a star.
Explanation:There are two different ways to understand time: solar time and sidereal time. Solar time is based on the position of the Sun in the sky and is used to determine the time of day. Sidereal time is based on the rotation of the Earth relative to the stars and is used to track the Earth's motion through space. An example of solar time is the time displayed on a sundial, which changes as the Sun moves across the sky. An example of sidereal time is the time displayed on a telescope tracking the motion of a star, which remains constant as the Earth rotates.
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"how do the fundamental laws of physics make manifest that space has 3 dimensions?"
What is the ultimate source of energies for fossil fuels, solar cells and windmills?
A golfer hits a shot to a green that is elevated 2.90 m above the point where the ball is struck. the ball leaves the club at a speed of 19.2 m/s at an angle of 50.0˚ above the horizontal. it rises to its maximum height and then falls down to the green. ignoring air resistance, find the speed of the ball just before it lands. v = entry field with incorrect answer now contains modified data entry field with correct answer
If you are in a rear-wheel skid, you must release your brakes and turn your steering wheel __________
a. into the direction of the skid.
b. opposite direction of the skid.
c. straight.
Answer:
a) into the direction of the skid
Explanation:
Suppose you throw a ball vertically downward with a speed of 10 m/s. neglecting air friction, what would be the speed of the ball one second later?
Answer:
The speed of the ball one second later is 19.8 m/s.
Explanation:
Given that,
Initial speed of the ball, u = 10 m/s
Let v is the speed of the ball after one second. The ball will move downward under the action of gravity, a = g
Using the first equation of motion as :
[tex]v=u+at[/tex]
[tex]v=u+gt[/tex]
[tex]v=10+9.8\times 1[/tex]
v = 19.8 m/s
So, the speed of the ball one second later is 19.8 m/s. Hence, this is the required solution.
Convection in the atmosphere is the process whereby air masses rise and fall, distributing heat and moisture over the planet.
a. True
b. False
If 20 beats are produced within a single second, which of the following frequencies could possibly be held by two sound waves traveling through a medium along a common path at the same time
A. 38 Hz and 63 Hz
B. 18 Hz and 26 Hz
C. 47 Hz and 55 Hz
D. 22 Hz and 42 Hz
The correct choice is
D. 22 Hz and 42 Hz.
In fact, the beat frequency is given by the difference between the frequencies of the two waves:
[tex] f_B = |f_1 -f_2| [/tex]
In this problem, the beat frequency is [tex] f_B=20 Hz [/tex], therefore the only pair of frequencies that gives a difference equal to 20 Hz is
D. 22 Hz and 42 Hz.
The ultimate source of energy that powers the sun is
The ultimate source of energy that powers the sun is the Mass energy of hydrogen fusing into helium, there is no other process than the annihilation of mass to give energy that has been advocated by Albert Einstein and it is capable of keeping the sun alive.
Answer:
Explanation:
At what condition the screw guage does not have zero error?
Argelia has a stack of schoolbooks sitting in the backseat of her car. When Argelia makes a sharp right turn, the books slide to the left of the seat until they come to a rest against the car door. Explain why this happens.
Answer:
The books slide to the left due to inertia, and then they come to a rest due to the force applied by the car door.
Explanation:
The entire motion of the books can be explained by using the first two laws of Newton:
- 1st Newton's law (also called Law of Inertia): an object at rest stays at rest and an object in motion stays in motion with constant velocity if no unbalanced forces act on it
- 2nd Newton's law: when an object is acted upon unbalanced forces, an acceleration is induced in the motion of the object, according to the equation
[tex]F=ma[/tex]
where F is the net force on the object, m is its mass and a is its acceleration.
Coming back to our problem:
- At the beginning, Argelia makes a sharp turn right. Due to the law of inertia, the books (which are not fixed to the car) continue their motion straight as it was before the curve: so, since the car is moving right, they appear to go the left of the car.
- When the books hit the car door, they stop moving due to the 2nd Newton's law: in fact, the car door applies an unbalanced force against the books, and as a result the books have a negative acceleration (=deceleration), so they slow down and eventually they stop.
The books moved due to the force that was applied and they came to rest due to inertia.
Inertia simply means the tendency to do nothing or to be able to remain unchanged. It is the resistance of any object to any change in the velocity of the object.
The books moved due to the force that was applied and they came to rest due to inertia. The book will be at rest as long as there's no force that acted on them.
In this case, the sharp turn of the car resulted in a force that acted on the car.
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Creative Commons Attribution-Share Alike 3.0 Unported Look at the graph. Where P is price and Q is quantity, what might cause a move from B to A? Fewer workers are needed to manufacture the product. A nationwide discount program is implemented. New technologies make manufacturing more efficient. Two other firms open to manufacture the same product.
Two soccer players kick the same 2-kg ball at the same time in opposite directions one kicks with a force of 15 n the other kicks with a force of 5 n what is the resulting acceleration of the ball in m/s2
Final answer:
The resulting acceleration of the soccer ball after being kicked in opposite directions by two players is 5 m/s^2, calculated using Newton's Second Law of Motion.
Explanation:
When two soccer players kick the same 2-kg ball in opposite directions with different forces, we calculate the resulting acceleration of the soccer ball by applying Newton's Second Law of Motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
In this scenario, one player kicks with a force of 15 N while the other kicks with a force of 5 N in the opposite direction. The net force on the ball is the difference between these two forces because they are applied in opposite directions. Therefore, the net force (Fnet) is:
Fnet = 15 N - 5 N = 10 N
To find the acceleration (a), we rearrange Newton's Second Law to solve for 'a':
a = Fnet / m
Substituting the values, we get:
a = 10 N / 2 kg = 5 m/s2
About 40 j is required to push a crate 4 m across a floor. if the push is in the same direction as the motion of the crate, the force on the crate is about
To calculate the force exerted on a crate, divide the work done (40 J) by the distance moved (4 m) to get 10 N.
Explanation:You have asked how much force is required to push a crate across a floor if it takes about 40 joules (J) to push the crate 4 meters (m). The force can be calculated using the work-energy principle, where the work done on an object is equal to the force applied times the distance over which the force is applied, assuming the force is constant and in the direction of motion. In formula terms, this is expressed as Work (W) = Force (F) × Distance (d).
To find the force, we rearrange the formula for work to solve for F: F = W/d. Substituting the given values, we have F = 40 J/4 m. Therefore, the force exerted on the crate is 10 Newtons (N).
What is the radius of a sphere with a surface area of 100πcm2? 10 cm 5 cm 25 cm 3 cm?
I think the answer is 5cm
Physics problem: piston? The piston of a hydraulic automobile lift is 0.300 m in diameter. 1. What gauge pressure, in pascals, is required to lift a car with a mass of 1200 kg?
What principle of joint operations entails expending minimum essential combat power on secondary efforts in order to allocate the maximum possoble combat power on primary efforts?
Which stars are composed of matter in which electrons have combined with protons?
Answer:
Neutron star
Explanation:
A neutron star is a giant star and a very condense core mainly consists of neutrons. It is one of the last stage of the star.
It is very small radius as compared to the other stars and it forms after the supernova explosion.
Although the mass of neutron star is not much large so that it becomes a black hole in future.