1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
alina1380 [7]
3 years ago
13

Determine the activity of the sample of cerium when the sample was 20 seconds old

Physics
1 answer:
Gre4nikov [31]3 years ago
7 0

Answer:

There are 3.779\times 10^{23} atoms when the sample of cerium is 20 seconds old.

Explanation:

The decay of isotopes is modelled after the following exponential expression:

N(t) = N_{o}\cdot e^{-\left(\frac{\ln 2}{t_{1/2}}\right)\cdot t } (1)

Where:

N_{o} - Initial number of atoms, dimensionless.

N(t) - Current number of atoms, dimensionless.

t - Time, measured in seconds.

t_{1/2} - Half-time, measured in seconds.

Now we clear the half-time within (1):

\ln \frac{N(t)}{N_{o}} = -\frac{t\cdot \ln 2}{t_{1/2}}

t_{1/2} = -\frac{t\cdot \ln 2}{\ln \frac{N(t)}{N_{o}} }

If we know that N_{o} = 5\times 10^{23}, N(t) = 2\times 10^{23} and t = 66\,s, then the half-life of the isotope is:

t_{1/2}=-\frac{(66\,s)\cdot \ln 2}{\ln \frac{2}{5} }

t_{1/2}\approx 49.927\,s

And the decay equation for the sample is described by:

N(t) = (5\times 10^{23})\cdot e^{-0.014\cdot t}

Lastly, if we get that t = 20\,s, then the activity of the sample of cerium is:

N(20) = (5\times 10^{23})\cdot e^{(-0.014)\cdot (20)}

N (20) \approx 3.779\times 10^{23}

There are 3.779\times 10^{23} atoms when the sample of cerium is 20 seconds old.

You might be interested in
Consider the points below. P(1, 0, 1), Q(−2, 1, 4), R(6, 2, 7) (a) Find a nonzero vector orthogonal to the plane through the poi
kozerog [31]

Answer:

a) (0, -33, 12)

b) area of the triangle : 17.55 units of area

Explanation:

<h2>a) </h2>

We know that the cross product of linearly independent vectors \vec{A} and \vec{B} gives us a nonzero, orthogonal to both, vector. So, if we can find two linearly independent vectors on the plane through the points P, Q, and R, we can use the cross product to obtain the answer to point a.

Luckily for us, we know that vectors \vec{A} = \vec{P}-\vec{Q} and \vec{B} = \vec{R} - \vec{Q} are living in the plane through the points P, Q, and R, and are linearly independent.

We know that they are linearly independent, cause to have one, and only one, plane through points P Q and R, this points must be linearly independent (as the dimension of a plane subspace is 3).

If they weren't linearly independent, we will obtain vector zero as the result of the cross product.

So, for our problem:

\vec{A} = \vec{P} - \vec{Q} \\\\\vec{A} = (1,0,1) - (-2,1,4)\\\\\vec{A} = (1 +2,0-1,1-4)\\\\\vec{A} = (3,-1,-3)

\vec{B} = \vec{R} - \vec{Q} \\\\\vec{B} = (6,2,7) - (-2,1,4)\\\\\vec{B} = (6 +2,2-1,7-4)\\\\\vec{B} = (8,1,3)

\vec{A} \times  \vec{B} = (A_y B_z - B_y A_z) \  \hat{i} - ( A_x B_z-B_xA_z) \ \hat{j} + (A_x B_y - B_x A_y ) \ \hat{k}

\vec{A} \times  \vec{B} = ( (-1) * 3 - 1 * (-3) ) \  \hat{i} - ( 3 * 3 - 8 * (-3)) \ \hat{j} + (3 * 1 - 8 * (-1) ) \ \hat{k}

\vec{A} \times  \vec{B} = ( - 3 + 3 ) \  \hat{i} - ( 9 + 24 ) \ \hat{j} + (3 + 8 ) \ \hat{k}

\vec{A} \times  \vec{B} = 0 \  \hat{i} - 33 \ \hat{j} + 12 \ \hat{k}

\vec{A} \times  \vec{B} =(0, -33, 12)

<h2>B)</h2>

We know that \vec{A} and \vec{B} are two sides of the triangle, and we also know that we can use the magnitude of the cross product to find the area of the triangle:

|\vec{A} \times  \vec{B} | = 2 * area_{triangle}

so:

\sqrt{(-33)^2 + (12)^2} = 2 * area_{triangle}

\sqrt{1233} = 2 * area_{triangle}

35.114= 2 * area_{triangle}

17.55 \ units \  of \ area =  area_{triangle}

5 0
3 years ago
Different kinds of lenses are used in eyeglasses to help people with eye conditions. Farsightedness is an eye condition in which
andriy [413]

Answer:

tyy

Explanation:

5 0
2 years ago
What part of a standing sound wave does a musician seek in playing a musical note of a specific pitch?
marusya05 [52]
The correct answer to the question above is that the magician is seeking the wavelength of the standing wave. The part of a standing sound wave, which is its wavelength, the magician is seeking when playing a musical note of a specific pitch. 
6 0
3 years ago
Read 2 more answers
Describe the gravity and magnetic separation technique using sand as an example​
Svet_ta [14]

Answer:

Gravity separation is an industrial method of separating two components, either a suspension, or dry granular mixture where separating the components with gravity is sufficiently practical: i.e. the components of the mixture have different specific materials and Magnetic separations take advantages of natural magnetic properties between minerals in feed. The separation is between economic ore constituents, noneconomic contaminants and gangue. and saw dust can be separated by gravity separation method. The process can be used for separating insoluble substances which are heavier than liquid by allowing them to settle down on their own due to gravity. The mixture of sand and iron can be separated from each other by using a magnet. Iron gets attracted towards a magnet leaving behind the sand.

<h2>Please mark me as brainliest by clicking on the crown at the bottom of my answer</h2>

4 0
3 years ago
What assumption can be made about the densities of two different spheres that have
Triss [41]

Answer:

Their densities are different as well

Explanation:

Density is worked out by dividing mass by volume. If the mass was the same then the densities would be as well. But it's not.

How many marks is this question?

8 0
3 years ago
Other questions:
  • A baby carriage is sitting at the top of a hill that is 21 m high. The carriage with the baby weighs 12 N. The carriage has pote
    11·1 answer
  • Calculate the magnitude of the electric field at one corner of a square 2.42 m on a side if the other three corners are occupied
    15·1 answer
  • In which galaxy is our solar system located?
    8·2 answers
  • A ball whose mass is 0.2 kg hits the floor with a speed of 4 m/s and rebounds upward with a speed of 3 m/s. if the ball was in c
    11·1 answer
  • What happens if two plates move away from each other?
    15·2 answers
  • Mass (kg)
    6·2 answers
  • Explain why people who use the drug in the following scenario might have potential health risks.
    5·2 answers
  • A boy throws rocks with an initial velocity of 12m/s [down] from a 20 m bridge into a river. Consider the river to be at a heigh
    5·1 answer
  • What do you call a substance that is usually dissolved in water?
    15·2 answers
  • Select the correct answer What are beats?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!