A sample contains 20 kg of radioactive material. The decay constant of the material is 0.179 per second. If the amount of time that has passed
is 300 seconds, how much of the of the original material is still radioactive? Show all work

Answers

Answer 1

Answer:

There are [tex]9.537\times 10^{-23}[/tex] kilograms of radioactive material after 300 seconds.

Explanation:

From Physics we know that radioactive materials decay at exponential rate, whose differential equation is:

[tex]\frac{dm}{dt} = -\lambda\cdot m[/tex] (1)

Where:

[tex]\frac{dm}{dt}[/tex] - Rate of change of the mass of the radioactive material, measured in kilograms per second.

[tex]m[/tex] - Current mass of the radioactive material, measured in kilograms.

[tex]\lambda[/tex] - Decay constant, measured in [tex]\frac{1}{s}[/tex].

The solution of the differential equation is:

[tex]m(t) = m_{o}\cdot e^{-\lambda\cdot t}[/tex] (2)

Where:

[tex]m_{o}[/tex] - Initial mass of the radioactive material, measured in kilograms.

[tex]t[/tex] - Time, measured in seconds.

If we know that [tex]m_{o} = 20\,kg[/tex], [tex]\lambda = 0.179\,\frac{1}{s}[/tex] and [tex]t = 300\,s[/tex], then the initial mass of the radioactive material is:

[tex]m(t) = (20\,kg)\cdot e^{-\left(0.179\,\frac{1}{s} \right)\cdot (300\,s)}[/tex]

[tex]m(t) \approx 9.537\times 10^{-23}\,kg[/tex]

There are [tex]9.537\times 10^{-23}[/tex] kilograms of radioactive material after 300 seconds.


Related Questions

need this answer in 30 minutes, What volume of ice is created from 200 cm3 of water?

Answers

217.4 cc it the answer

Answer:

i think about 218 cm3

Explanation:

water expands by about 9% when it freezes so 200* 1.09=218

\

Not sure if I'm correct though

PLS HELP ITS WORTH SO MANY POINTS AHH
LONGITUDINAL
SURFACE
TRANSVERSE
HEAT

Answers

Answer:

C. transverse

Which example illustrates Newton's second law?
A. A wheelbarrow remains stationary when no one pushes on it.
B. More mass is added to a wheelbarrow, and a larger force is
required to move it.
C. A person pushes a wheelbarrow, causing it to move forward.
D. The force of a wheelbarrow on the ground is equal to the force of
the ground on the wheelbarrow.

Answers

Answer:B

Explanation:

Mass

More mass is added to a wheelbarrow, and a larger force is required to move it - illustrates Newton's second law.

What is force?

An object's push or pull is seen as exerting a force. The interaction of the objects produces push and pull. You can also use words like stretch and squeeze to describe force.

The definition of force in physics is: The push or pull on a mass-containing item changes its velocity.

Newton’s second law of motion states that “Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration."

Hence more mass is added to a wheelbarrow, and a larger force is required to accelerate, i.e., move it.

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A 100 Watt lightbulb uses 360000 Joules ever hour. How many lightbulbs could be powered for one hour by the energy from the Hiroshima bomb?

Answers

Answer:

200 million electric light bulbs.

Explanation:

First, we must calculate the power of the electric bulb, for this, we use the following equation that relates the energy as a function of time.

[tex]P=E/t[/tex]

where:

P = power [W] (units of watts)

E = energy = 360000 [J] (units of Joules)

t = time = 1 [h] = 3600 [s]

[tex]P = 360000/3600\\P= 100[W][/tex]

In 1 hour 1 electric lightbulb produces 100 [W], now we need to know the amount of energy produced by the Hiroshima bomb. A search made by the internet give us the data of 20 [GW] or [Gigawatts].

We need to remember that 1 Giga = 1 x10⁹

Energy Hiroshima explosion= 20*10⁹[W]

Amount = (20x10⁹)/100

Amount = 200 x10⁶ [bulbs]

That is, we would need an amount of 200 million electric light bulbs.

A cannon is fired with an initial horizontal velocity of 20 m/s and initial vertical velocity of 25 m/s. After 3s in the air, the canon hits its target. How far away was the canon from its Target?

Answers

Answer:

140.16m

Explanation:

To get the distance the cannon is away from its target, we will apply the equation of motion;

S = ut + 1/2gt²

u is the resultant initial velocity

g is the acceleration due to gravity

t is the time taken.

Given

g = 9.8m/s²

t = 3s

u = √20²+25²

u = √400+625

u = √1025

u = 32.02m/s

Substitute the values into the formula and get the distance S;

S = 32.02(3)+ 1/2(9.8)3²

S = 96.06+44.1

S = 140.16m

Hence the cannon was 140.16m away from its target

What happens to the kinetic energy of a hot drink when an ice cube is put into the drink?

Answers

Answer:

Heat is kinetic energy -- the higher the temperature of a substance, the faster and farther its molecules move.

Explanation:

... Conversely, when heat transfers from your beverage to the ice and the temperature of the liquid drops, the molecules in the beverage slow down. When those molecules slow down, their kinetic energy decreases.

. Which color has the shortest wavelength? *
2 points
a. Violet
b. Yellow
c. Blue
d. Red

Answers

Answer:

Violet

Explanation:

Occurring to Google red has the longest while violet has the shortest. Violet is the shortest at 380 nanometers.

Answer:

violet

Explanation:

Violet has the shortest light wavelength.

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Question 3 of 10
Why do electric charges that move through a magnetic field produce an
electric current?
A. The magnetic field exerts a force on only the negative charges in
the wire.
B. The magnetic field exerts a force on only the positive charges in
the wire.
C. The magnetic field pushes negative charges and positive charges
in the same direction.
D. The magnetic field pushes negative charges and positive charges
in opposite directions.

Answers

Answer: D

Explanation: a p e x :)

Answer:

B. The magnetic field pushes negative charges and positive charges in opposite directions.

15. Which element will donate electrons?
nitrogen
chlorine
aluminum
sulfur

Answers

I think its nitrogen sorry if I’m wrong

A 860g block of titanium metal has a volume of 200 cm3 and the density of 4.3g/cm^3.
What would be the density of the block of titanium metal if the volume of the block was 500 cm3 and the mass of the
block was 2150g?

Answers

Answer:

4.3 g/ cm^3

Explanation:

Mass / Volume = density . so 2150/500= 4.3 g/cm^3

A robin flies a distance of 45963 cm. How far has it flown in kilometers?

Answers

Answer:

0.46km

Explanation:

45963cm/100cm=459.63m/1000m=0.45963 or 0.46km

a car starts from rest and accelerates to a speed of 30 m/s in a time of 3 seconds. the average acceleration of the car is

Answers

Answer:

10m/s²

Explanation:

v=u+at

30=0+a(3)

∴a=10m/s²

Answer:

10m/s^2. Just curious, what kind of car is it? Is it a lamborghini

Explanation:

An elevator is being pulled up from the ground floor to the third floor by a cable. The cable is exerting 4500 newtons of force on the elevator. According to Newton's law of action-reaction, what is the gravitational force on the elevator, in newtons, if the elevator is NOT accelerating?

Answers

Answer:

The gravitational force on the elevator = 4500N

Explanation:

The given parameters are;

The force applied by the elevator, F  = 4500 N

The acceleration of the elevator = Not accelerating

From Newton's third law of motion, the action of the cable force is equal to the reaction of the gravitational force on the elevator which is the weight, W and motion of the elevator as follows;

F = W + Mass of elevator × Acceleration of elevator

∴ F = W + Mass of elevator × 0 = W

F = 4500 N = W

The net force on the elevator is F - W = 0

The gravitational force on the elevator = W = 4500N.

The gravitational force on the elevator, if the elevator is NOT accelerating is 4500 N.

Given data:

The magnitude of force on the elevator is, F = 4500 N.

From Newton's third law of motion, the action of the cable force is equal to the reaction of the gravitational force on the elevator which is the weight, W and motion of the elevator as follows,

F = W + ma

Here, a is the acceleration of the elevator. Since, the elevator is not accelerating. Then, a = 0 .

The weight of the elevator is due to the gravitational force. So, we need to obtain the weight as gravitational force.

Solving as,

[tex]F = W+ma\\\\F=W +(m \times 0)\\\\4500=W\\\\W = 4500 \;\rm N[/tex]

Thus, we can conclude that the gravitational force on the elevator, if the elevator is NOT accelerating is 4500 N.

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emotional symptoms that may occur in those with a schizophrenic Disorder generally include all of the following except ______ emotion.
A. Flat
B. Appropriate
C. No
D. Inappropriate

Answers

Answer:

B

Explanation:

edge 2020

The emotional symptoms that may occur in those with a Schizophrenic disorder generally include all of the following except appropriate emotion. Hence, option (B) is correct.

What is schizophrenic disorder?

Schizophrenia is a persistent, severe mental illness that has an impact on a person's relationships with others as well as their thinking, acting, and emotional expression. Despite not being as prevalent as other severe mental illnesses, schizophrenia can be the most persistent and incapacitating.

Schizophrenia patients frequently struggle to function well in relationships, the workplace, and academic settings. They can appear to have lost their sense of reality, feel afraid and withdraw. This chronic illness cannot be cured, but it can be managed with the right care.

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Un montañero de 65kg de masa ha ascendido a la cima del Everest, la montaña más alta del mundo de 8848m de altura sobre el nivel del mar. Calcula el trabajo que ha realizado para subir los últimos 500m

Answers

Answer:

El trabajo realizado para subir los últimos 500 metros es 318727,5 joules.

Explanation:

Por la definición de trabajo sabemos que el montañero debió contrarrestar trabajo causado por la gravedad terrestre. Si asumimos que el cambio de la altura es muy pequeño en comparación con el radio del planeta (6371 kilómetros vs. 0,5 kilómetros), entonces podemos considerar que la aceleración gravitacional es constante y la ecuación de trabajo ([tex]\Delta W[/tex]), medido en joules, que reducida a:

[tex]\Delta W = m\cdot g\cdot \Delta z[/tex] (1)

Donde:

[tex]m[/tex] - Masa del montañero, medido en kilogramos.

[tex]g[/tex] - Aceleración gravitacional, medida en metros por segundo al cuadrado.

[tex]\Delta z[/tex] - Distancia vertical de ascenso del montañero, medida en metros.

Si tenemos que [tex]m = 65\,kg[/tex], [tex]g = 9,807\,\frac{m}{s^{2}}[/tex] y [tex]\Delta z = 500\,m[/tex], entonces el trabajo realizado por el montañero para subir es:

[tex]\Delta W = (65\,kg)\cdot \left(9,807\,\frac{m}{s^{2}} \right)\cdot (500\,m)[/tex]

[tex]\Delta W = 318727,5\,J[/tex]

El trabajo realizado para subir los últimos 500 metros es 318727,5 joules.

1. Some penguins are playing turtle hockey on the frictionless ice. Ramona the penguin hits the turtle

with a force of magnitude F, and the turtle experiences an acceleration of magnitude a (Fand a are of

unknown size). Francisco the penguin hits the same turtle with a force of magnitude three times

greater than Ramona's force (3F). What will the resulting acceleration of the turtle be? Answer in

terms of a. Support your answer with reasoning and reference to Newton's Second Law.

Answers

Answer:

a' = 3a

Explanation:

Newton's Second Law gives the magnitude of the unbalanced force applied to an object as follows:

F = ma

where,

F = Force Applied

m = Mass of Object

a = acceleration

FOR RAMONA'S PUSH:

F = F

m = m

a = a

Therefore,

F = ma  

a = F/m   ---------------- equation (1)

FOR FRANSICO'S PUSH:

F = 3F

m = m  (mass of turtle will be same)

a = a'

Therefore,

3F = ma'  

a' = 3F/m

using equation 1

a' = 3a

A falling object is said to reach a constant velocity (terminal velocity)..

a. when there is no gravitational force acting on it.

b. when there is no air resistance acting on it.

c. when air resistance equals the acceleration of gravity on it.

d. when it stops falling.

Answers

C

Terminal velocity is the maximum velocity attainable by an object as it falls through a fluid (air is the most common example). It occurs when the sum of the drag force (Fd) and the buoyancy is equal to the downward force of gravity (FG) acting on the object.(Wikipedia)




Newton's first law of motion states than an object's motion will not change
unless?

Answers

Answer:

it is hit by an external force

Explanation:

A stone is thrown vertically upwards. It takes 2 seconds to reach it highest point the acceleration due to gravity is 10m/s. With what velocity must it be thrown ?

Answers

Answer:

The velocity the stone must be thrown with is 20 m/s.

Explanation:

Given;

time taken for the stone to reach it highest point, t = 2 s

acceleration due to gravity, g = 10 m/s²

The maximum height reached by the stone at the given time is calculated as;

[tex]h = \frac{1}{2}gt^2\\\\h = \frac{1}{2}*10*2^2\\\\h = 20 \ m[/tex]

Determine the initial of the stone;

v² = u² + 2gh

where;

v is the final velocity of the stone at maximum height = 0

u is the initial velocity of the stone = ?

0 = u² - 2(10 x 20)

0 = u² - 400

u² = 400

u = √400

u = 20 m/s

Therefore, the velocity the stone must be thrown with is 20 m/s.

what is an isoelectronic series

Answers

Answer:

A comparison of the dimensions of atom an ions that have the same number of electron but different nuclear charges is called isoelectronic series

Answer:

A comparison of the dimensions of atoms or ions that have the same number of electrons but different nuclear charges, called an isoelectronic series, shows a clear correlation between increasing nuclear charge and decreasing size

Cody’s car accelerates from 0m/s to 65 m/s northward in 25 seconds. What is the acceleration of the car?

Answers

Answer:

v=v(initial)+at

45=0+15a

a= 3m/sec²

Explanation:

edge 2020

You throw an orange out a window at a height of 12.00 meters
upwards at an angle of 32° to the horizontal at a velocity of 3.5
m/s. What is the maximum height that the orange will reach?

Answers

Answer:

12.18

Explanation:

The maximum height that the orange will reach is 12.18 m.

What is projectile?

When an object is thrown at an angle from the horizontal direction, the object is said to be in projectile motion.

You throw an orange out a window at a height of 12.00 meters upwards at an angle of 32° to the horizontal at a velocity of 3.5 m/s.

If u is the initial speed, the maximum height of the ball from the point of throwing is

H = u² sin²θ / 2g

Put the values, we get

H = 3.5² sin²32° / (2x9.81)

H = 0.1753 m

So, the maximum height calculated from the ground is

12 + 0.18 = 12.18 m

Thus ,the maximum height that the orange will reach is 12.18 m.

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7. In what ways has science harmed us?​

Answers

Answer: At several different levels, scientific awareness will enhance the quality of life, from the routine functioning of our daily lives to global issues. In energy, conservation, agriculture, health, transportation, communication, security, economics, recreation, and discovery, science informs public policy and personal decisions.

Explanation:

Hope This Helps! : )

Select the correct answer.
Which statement about pneumatic systems is true?
A.
Pneumatic systems generate greater force than hydraulic systems.
B.
Pneumatic systems are safe to use at any level of pressure.
C.
Pneumatic systems are more expensive than hydraulic systems.
D.
Pneumatic systems are cleaner than hydraulic systems.

Answers

Statement D about pneumatic systems is true. Pneumatic systems are cleaner than hydraulic systems.

What is the pneumatic system?

Pneumatic systems are employed in a wide range of manufacturing and assembly applications. They can be used to transport objects on production lines as well as in maintenance facilities.

In hydraulic systems liquid is used as fluid for the force transmission. While in the pneumatic system air is used causing more cleanliness in the system.

The pneumatic systems are cleaner than hydraulic systems.

Hence, a statement D about pneumatic systems is true.

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1. If all four switches below are turned on, which light bulb will light up? (W is wood, S is silver, and Yis yarn.)
A.Circuit A
B. Circuit B
C. Circuit C
D. Circuit D

Answers

The answer to this question is d- circuit D

The correct option is option (c).

The bulb in the circuit C will glow up.

Complete circuit:

We know that for the light bulb to glow up, there must be finite current flowing in the circuit through the bulb.

But, for the current to flow in the circuit, first, the circuit must be complete.

As we can see in the figure provided in the question, circuit A is not complete, whereas circuit B, C, and D are complete. So from here we can reject the circuit A.

Now, the circuit B contains wood, circuit C contains silver and circuit D contains yarn. Only silver is an electrical conductor.

Therefore, circuit C is complete and current will flow through the bulb and it will glow up.

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When sand absorbs the electromagnetic waves of the Sun, it becomes warm through the process of______.

radiation


conduction


convection


evaporation

Answers

The answer is radiation I believe

radiation

  i know because i know

surface?
What is the mass of an object that experiences a gravitational force of 700 N near the Earth's surface

Answers

Answer:

70kg

Explanation:

Given parameters:

Gravitational force  = 700N

Unknown:

Mass of the person = ?

Solution:

The weight is gravitational force on the person and can be expressed as;

        W = mg

m is the mass

g is the acceleration due to gravity  = 10m/s²

 So;

        700 = m x 10

            m  = 70kg

El extremo de una cuerda se mueve de tal manera que las partículas de la cuerda emplean 0.25 segundos para producir una vibración. ¿Cuál es el periodo? Y ¿Cuál es la frecuencia de la vibración producida

Answers

Responder:

T = 0.25 segundos

f = 4 Hz

Explicación:

Paso uno:

datos dados

se nos dice que las partículas tardan 0,25 segundos en completar una vibración

por lo tanto, el período es de 0,25 segundos

¿Qué es un período de vibración?

Un período T es el tiempo necesario para que un ciclo completo de vibración pase por un punto determinado.

la expresión para el período se da a continuación.

T = 1 / f

¿Cuál es la frecuencia de vibración?

Básicamente, se refiere a la frecuencia con la que ocurren las vibraciones.

la frecuencia es una tasa, se expresa como la inversa del período

f = 1 / T

t = 1 / 0.25

f = 4 Hz

The diagram shows the forces acting on an object at an instant of time. Which of
the following statements about the forces is true? Select one answer.

Answers

Answer:

The correct option is;

The object is in horizontal equilibrium but NOT in vertical equilibrium

Explanation:

The given given forces in the force diagram are expressed in vector form as follows;

Topmost force = 2·i + 3·j

The horizontal force = 3·i

The force at the lower section = -5·i - 2·j

Adding the forces together to find the resultant force gives;

[tex]F_R[/tex] = 2·i + 3·j + j + (-5·i - 2·j) = 5·i + 3·j - 5·i - 2·j = i + j = j

[tex]F_R[/tex] = j

Therefore, the horizontal component of the forces are balanced as they cancel out and the object is said to be in horizontal equilibrium

However, the object has a net total resultant force component in the positive vertical direction, the object is not in vertical equilibrium.

Motion of a potter's wheel is an example of
motion​

Answers

Answer:

bus , running boy etc

Explanation:

moving body is called motion .

e.g. running boy , bus, birds flying etc

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