Answer:
Explanation:
Half-life problems are modeled as exponential equations. The half-life formula is [tex]P=P_o\left (\dfrac{1}{2} \right)^{\frac{t}{k}}[/tex] where [tex]P_o[/tex] is the initial amount, [tex]k[/tex] is the length of the half-life, [tex]t[/tex] is the amount of time that has elapsed since the initial measurement was taken, and [tex]P[/tex] is the amount that remains at time [tex]t[/tex].
[tex]P=14.2\left (\dfrac{1}{2} \right)^{\frac{t}{8.0252}}[/tex]
Deriving the half-life formula
If one forgets the half-life formula, one can derive an equivalent equation by recalling the basic an exponential equation, [tex]y=a b^{t}[/tex], where [tex]t[/tex] is still the amount of time, and [tex]y[/tex] is the amount remaining at time [tex]t[/tex]. The constants a and b can be solved for as follows:
Knowing that amount initially is 14.2g, we let this be time zero:
[tex]y=a b^{t}[/tex]
[tex](14.2)=ab^{(0)}[/tex]
[tex]14.2=a *1[/tex]
[tex]14.2=a[/tex]
So, [tex]a=14.2[/tex], which represents out initial amount of the substance, and our equation becomes: [tex]y=14.2 b^{t}[/tex]
Knowing that the "half-life" is 8.0252 days (note that the unit here is "days", so times for all future uses of this equation must be in "days"), we know that the amount remaining after that time will be one-half of what we started with:
[tex]\left(\frac{1}{2} *14.2 \right)=14.2 b^{(8.0252)}[/tex]
[tex]\dfrac{7.1}{14.2}=\dfrac{14.2 b^{8.0252}}{14.2}[/tex]
[tex]0.5=b^{8.0252}[/tex]
[tex]\sqrt[8.0252]{\frac{1}{2}}=\sqrt[8.0252]{b^{8.0252}}[/tex]
[tex]\sqrt[8.0252]{\frac{1}{2}}=b[/tex]
Recalling exponent properties, one could find that [tex]\left ( \frac{1}{2} \right )^{\frac{1}{8.0252}}=b[/tex], which will give the equation identical to the half-life formula. However, recalling this trivia about exponent properties is not necessary to solve this problem. One can just evaluate the radical in a calculator:
[tex]b=0.9172535661...[/tex]
Using this decimal approximation has advantages (don't have to remember the half-life formula & don't have to remember as many exponent properties), but one minor disadvantage (need to keep more decimal places to reduce rounding error).
So, our general equation derived from the basic exponential function is:
[tex]y=14.2* (0.9172535661)^t[/tex] or [tex]y=14.2*(0.5)^{\frac{t}{8.0252}}[/tex] where y represents the amount remaining at time t.
Solving for the amount remaining
With the equation set up, substitute the amount of time it takes to cross the Pacific to solve for the amount remaining:
[tex]y=14.2* (0.9172535661)^{(31.8)}[/tex] [tex]y=14.2*(0.5)^{\frac{(31.8)}{8.0252}}[/tex]
[tex]y=14.2* 0.0641450581[/tex] [tex]y=14.2*(0.5)^{3.962518068}[/tex]
[tex]y=0.9108598257[/tex] [tex]y=14.2* 0.0641450581[/tex]
[tex]y=0.9108598257[/tex]
Since both the initial amount of Iodine, and the amount of time were given to 3 significant figures, the amount remaining after 31.8days is 0.911g.
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Imagine that a single cell below goes through four cell divisions.
How many cells are produced? To find out, draw the parent cell
and cells present after each division. Then write the number of
cells in the space below each drawing. (Hint: the number of cells
doubles with each division.)
Two, four, eight and sixteen cells are produced from first, second, third and fourth cell division respectively.
How many cells are produced?When the body cell passes through cell division process, it divides into two daughter cells. In the second cell division, two cells divides into four cells. In the third cell division, the four cells divides into eight cells. In the fourth cell division, the eight cells divides and sixteen cells are produced.
So we can conclude that two, four, eight and sixteen cells are produced from first, second, third and fourth cell division respectively.
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what is the frequency of the photon emitted by a hydrogen atom when its electron drops from the n = 6 to n = 4 energy level?
The frequency of the photon emitted by a hydrogen atom is [tex]26.2*10^-^4 hz[/tex]
What are Photons?A particle representing a quantum of light or other electromagnetic radiation. A photon carries energy proportional to the radiation frequency but has zero rest mass.
In the case of light, the frequency, symbolized by the Greek letter nu (ν), of any wave equals the speed of light, c, divided by the wavelength λ:
v = c/λ
Since the wavelength λ is in the bottom of the fraction, the frequency is inversely proportional to the wavelength.
v = c/λ
v= [tex]\frac{3*10^8}{434*10^-^9} = 6.91*10^1^4 Hz[/tex]
By using Rydberg's formula,
1/λ [tex]= Rz^2(\frac{1}{n_1^2} - \frac{1}{n_2^2})[/tex]
1/λ = [tex]109677 *(\frac{1}{4^2} - \frac{1}{6^2}) = 3808.22 cm^-^1[/tex]
λ = [tex]26.2*10^-^4 hz[/tex]
[tex]26.2*10^-^4 hz[/tex] is frequency of the photon emitted by a hydrogen atom.
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The following equation shows the position of a particle in time t, x=at2i + btj where t is in second and x is in meter. A=2m/s2, b=1m/s.
Find
A, the average velocity of the particle in the time interval t₁=2sec and t₂=3sec
B, the velocity and acceleration at any time t.
C, the average acceleration in the time interval given in part (a)
(a) The average velocity of the particle in the time interval t₁=2sec and t₂=3sec is 10 m/s.
(b) The velocity and acceleration at any time t is v = (4ti + j) m/s and a = a = 4i m/s²
(c) The average acceleration in the time interval given in part (a) is 3.98 m/s².
Position of the particlex = at²i + btj
x = 2t²i + tj
Average velocity, at t₁=2sec and t₂=3secΔv = Δx/Δt
x(2) = 2(2)²i + 2j
x(2) = 8i + 2j
|x(2)| = √(8² + 2²) = 8.246
x(3) = 2(3)²i + 3j
x(3) = 18i + 3j
|x(3)| = √(18² + 3²) = 18.248
Δv = (18.248 - 8.246)/(3 - 2)
Δv = 10 m/s
Velocity and acceleration at any time, tv = dx/dt
v = (4ti + j) m/s
a = dv/dt
a = 4i m/s²
Average accelerationv(2) = 4(2)i + j
v(2) = 8i + j
|v(2)| = 8.06 m/s
v(3) = 4(3)i + j
v(3) = 12i + j
|v(3)| = 12.04 m/s
a = (12.04 - 8.06)/(3 - 2)
a = 3.98 m/s²
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A mass of (200 g) of hot water at (75.0°C) is mixed with cold water of mass M at (5.0°C). The final temperature of the mixture is (25.0°C). What is the mass of the cold water (M)?
Answer:
500 g
Explanation:
Specific heat of water = 1 j/g-c
Heat given up by hot water = 200(75-25)(1) = 10 000 j
this is the heat GAINED by the cold water
10000 j = x ( 25 -5)(1)
x =500g
A 2100-W hair dryer is operated on a 120-V
circuit for 12 min. If electricity
costs $0.25/kWh, what was the cost (in
cents) of using the blow dryer? Round final
answer to the nearest cent.
Answer:
cost=$15
Explanation:
given;
P= 2100 W
t= 12'= 720 sec=0.2h
V= 120 V
required;
Energy?
cost?
solution;
Energy(kWh) = power*time(in hour)
E=2100*0.2= 420 kWh
cost= 420 kWh* $0.25/kWh
cost= $15
since blow dryer use 120-V
A 3,204 kg tree positioned on the edge of a cliff 247 m above the ground breaks away and falls into the valley below which is considered zero potential energy. If the tree’s mechanical energy is conserved, what is the speed of the tree just before it hits the ground in meters/sec?
Let's see
PE is turned to KE as per law of conservation of energy[tex]\\ \rm\Rrightarrow mgh=\dfrac{1}{2}mv^2[/tex]
[tex]\\ \rm\Rrightarrow 2gh=v^2[/tex]
[tex]\\ \rm\Rrightarrow 2(10)(247)=v^2[/tex]
[tex]\\ \rm\Rrightarrow v²=4940[/tex]
[tex]\\ \rm\Rrightarrow v=70.3ms^{-1}[/tex]
what is the energy of a photon with a frequency of 8.34 x 10^14 hz, in joules?
Answer:
E = 5.52 x 10⁻¹⁹ J
Explanation:
The formula for energy of a photon, E, is:
[tex]E = hf[/tex]
where h is Plank's constant = 6.62 x 10 ⁻³⁴ .
Using the formula:
E = 6.62 x 10⁻³⁴ x 8.34 x 10¹⁴
= 5.52 x 10⁻¹⁹ J
What is the spring constant if 85.0J of energy is stored when a spring is compressed 0.400m?
A.1060N/m
B.212N/m
C.531N/m
D.425N/m
Answer:
212N/m
Explanation:
First of all, what is spring constant
As per Hooke's law, The restoring force applied by the spring is proportional to the change in length, and restoring force is directed towards the equilibrium position. The proportionality constant is called the spring constant and it is a measure of the stiffness of the spring. So as Hooke's law
F = -Kx
Where
F -> Restoring force
K-> Spring constant
x -> change in length
the negative sign indicates it is acting toward the center
Rearranging this for the Spring constant, Spring constant formula is given by
k = Fx
Unit of Spring Constant is Newton/meter
Places rich in limestone and gypsum have hard water . why ??
Answer:
Hard water is formed when water percolates through deposits of limestone, chalk or gypsum which are largely made up of calcium and magnesium carbonates, bicarbonates and sulfates.
Explanation:
Hard water is formed when water percolates through deposits of limestone, chalk or gypsum which are largely made up of calcium and magnesium carbonates, bicarbonates and sulfates.
Answer:
Hard water indicates a high amount of minerals.
Explanation:
This most often occurs when natural water sources pass through mineral deposits such as limestone or chalk. The process leads to a relatively high level of calcium, iron, and magnesium.
Most of the bending of light in the eye is done at the air-cornea interface. By what angle (θcornea) is the beam of light shown in Figure deviated as it passes from air to the cornea if the incident angle is θi = 23.6°? The refractive index of air is nair = 1.00, the refractive index of the cornea is ncornea = 1.38. Explain why θcornea< θi?
The angle (θcornea) when light passes from air to cornea is 16.86°
What is Snell's law?It states that the ratio of sine of angle of incidence and angle of refraction is equal to the refractive index of second medium to the first medium.
sini/sinr =n₂ / n₁
Most of the bending of light in the eye is done at the air-cornea interface. The beam of light deviated as it passes from air to the cornea if the incident angle is θi = 23.6°.
Given the angle of incidence i = 23.6°, refractive index of air n₁ =1, refractive index of cornea n₂ = 1.38, then the angle of refraction at cornea is
sinr = sini x (n₁/n₂)
Plug the values, we get
sinr = sin23.6 x (1/1.38)
sinr = 16.86°
The angle of refraction is less than angle of incidence due to refraction.
Thus, the angle (θcornea) when light passes from air to cornea is 16.86°
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A snowboarder on a slope starts from rest and reaches a speed of 4.2 m/s after 7.3 s
The car's acceleration will be 0.575 m/s².The unit of acceleration is m/sec².
What is acceleration?The rate of velocity change concerning time is known as acceleration.
Given data;
Initial velocity, u= 0 m/s
Final velocity, v= 4.2 m/s
Time elapsed, t = 7.3 seconds.
To find ;
Acceleration, a
The acceleration when the change in velocity is observed by the formula as:
a= (v-u)/(t)
Substitute the given values:
a= (4.2-0)/(7.3)
a=(4.2)/(7.3)
a= 0.575 m/s²
Hence, the car's acceleration will be 0.575 m/s².
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Can you put this image back together? Type the correct order of letters below.
Answer:
CABD
.....................
The image is cut and jumbled and placed into different places, so the correct order of the image that it can be back together is CABD.
What is an image?A specific piece of something is an image. It can provide information to the optical system in two dimensions, three components, or in another way. An item that mimics a subject, such as a picture or other two-dimensional image, might be considered an image. An image in the context of signal analysis is a dispersed color amplitude.
A graphical image need not make use of the complete visual system. A common illustration of this is a grayscale image, which does not employ color, but instead relies on the visual game's sensitivity to brightness across all wavelengths. Even if it doesn't make proper use of the visual system, a black-and-white and white visual depiction of something is nonetheless an image.
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A 0.6 kg ball moving to the right at 12 m/s makes a head on elastic collision with a 0.3 kg ball traveling to the left at 3 m/s.
The velocity of the 0.6 kg ball initially after the collision is
Jason while driving on Kukum highway at 70 m.s – 1 seeing the traffic light turn red, he applies the brake and comes to rest in a time of 2 seconds. What is his deceleration?
Answer:
35 m/s^2
Explanation:
Decceleration = change in velocity / change in time
= ( 70 m/s ) / 2 seconds = 35 m/s^2
DEcceleration = 35 m/s^2
Jason's speed changes by - 35 m/s^2
The pressure of a gas (relative to vacuum) inside a rigid container at 0 °C is:
A) The same as at 25 °C.
B) Not zero, but somewhat less than it would be at 25 °C.
C) zero
The pressure of a gas inside a rigid container at 0 °C will not be zero, but will somewhat be less than it would be at 25 °C.
Temperature and pressure of gasesAccording to Charle's law of gases, the pressure of a gas is directly proportional to its temperature. This is based on the condition that the volume of the gas does not change.
Thus, for a gas inside a rigid container, the pressure at 0 °C may not be zero. However, the pressure will be less than it would be if the temperature were to be 25 °C.
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Name the inertia in the following cases.
A passenger jumping out of a moving bus falls forward.
Answer:
inertia of motion
Explanation:
it's because when a passenger is jumping from a bus his/her body is in motion after falling in a road he/she remains or tends to remain in the state of motion that is the reason
The value of acceleration due to gravity (g) on a point 10,000 kilometers above sea level is about 1.49 meters/second2. How much will an object, which weighs 98 newtons on the surface of Earth, weigh on this point? The value of acceleration due to gravity on Earth is 9.8 meters/second2.
An object, which weighs 98 N on the surface of Earth, weigh on this point is 2.23 x 10²⁴ kg.
What is gravity?The force of attraction felt by a person at the center of a planet or Earth is called as the gravity.
Given, the Earth has the acceleration due to gravity, g = 9.81 m/s².
Force of gravity W = mass x acceleration due to gravity
98N = m x 9.8m/s²
m = 10 kg
The value of acceleration due to gravity (g) on a point 10,000 km above sea level is about 1.49 m/s².
The acceleration due to gravity and mass is related as
g = GM/R²
where G = gravitational constant = 6.67 x 10⁻¹¹ N.m²/kg² and R is the distance between two masses.
Substituting the values, we get
1.49 m/s² = 6.67 x 10⁻¹¹ N.m²/kg² x M/ (10000 x 10³ m)²
M = 2.23 x 10²⁴ kg
Therefore, an object will weigh on this point is 2.23 x 10²⁴ kg
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The resistivity of pure water is fairly high, 1.8 × 105 Ω·m, whereas the resistivity of sea water is a million times lower, 2 × 10-1 Ω·m. Why does the high salt concentration make sea water significantly less resistive (i.e. more conductive) than pure water?
The high salt concentration make sea water significantly less resistive than pure water due to presence of charged ions in the sea water.
What is resistivity?The resistivity of a substance is the opposition to the flow of charges offered by the substance.
The greater the resistivity of a substance, the lesser its conductivity.
A high salt concentration make sea water highly conductive due to presence of charged ions in the water. The greater conductivity reduces the resistivity of the sea water.
A pure water has no charged ions in the water, thereby decreasing its conductivity and increasing its resistivity.
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How much heat is required to convert 12.0 g of ice at -10.0°C to steam at 100.0°C. Express your answer in joules, calories, and Btu.
