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1 year ago

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A radioactive isotope has a half-life of 2 hours. If a sample of the element contains 600,000 radioactive nuclei at 12 noon, how

many radioactive nuclei would be left at 6 pm?

1 answer:

storchak [24]1 year ago

7 0

Answer: There will be 75258 nuclei left at 6 pm.

Explanation:

a) half-life of the radioactive substance:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$t_{\frac{1}{2}}=\frac{0.69}{k}$

$k=\frac{0.69}{t_{\frac{1}{2}}}=\frac{0.693}{2hours}=0.346hours^{-1}$

b) Expression for rate law for first order kinetics is given by:

$A=A_0e^{-kt}$

where,

k = rate constant

t = time for decomposition = 6 hours ( from 12 noon to 6 pm)

A = activity at time t = ?

$A_0$ = initial activity = 600, 000

$A=600000\times e^{-0.346\times 6}$

$A=75258$

Thus there will be 75258 nuclei left at 6 pm.

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Hippos spend much of their lives in water, but amazingly, they don’t swim. manatees, They have, like little very body fat. The d

kenny6666 [7]

Answer:

428.59 N

Explanation:

Buoyant force, $B=Vg\rho$ where V is volume, g is gravitational constant and \rho is density

$B+F_{upward}=mg$ where $F_{upward}$ is upward force

$Vg\rho_{w}+F_{upward}=mg$

$F_{upward}=mg- Vg\rho_{w}$

$F_{upward}=g(mg- V\rho_{w})=g(m-m\frac {\rho_{w}{\rho_{hippo}}$ where $\rho_{hippo}$ is the density of hippo

$F_{upward}=mg(1-\frac {\rho_{w}}{\rho_{hippo}})$

Using g as 9.81

$F_{upward}=1500*9.81*(1-1000/1030)= 428.5922 N$

Therefore, the upward force=428.59 N

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2 years ago

A stone is thrown horizontally from 2.4m above the ground at 35m/s. The wall is 14m away and 1m high.At what height the stone wi

KIM [24]

The stone reaches the wall at a height of <u>1.62 m</u>.

The stone lands at a point <u>24.5 m</u> from the point of projection.

The stone is projected horizontally with a velocity u at a height <em>h</em> from the ground. The wall is located at a distance <em>x</em> from the point of projection. The stone takes a time <em>t</em> to reach the wall and in the same time the stone falls a vertical distance <em>y</em>.

The horizontal distance <em>x</em> is traveled with a constant velocity <em>u</em>.

$x=ut$

Calculate the time taken <em>t</em>.

$t=\frac{x}{u} \\ =\frac{14m}{35 m/s} \\ =0.40s$

The stone's initial vertical velocity is zero. It falls through a distance <em>y</em> in the time <em>t</em> under the action of acceleration due to gravity <em>g</em>.

$y=\frac{1}{2} gt^2\\ \frac{1}{2} (9.81m/s^2)(0.40s)^2\\ =0.784m$

The height <em>h₁ </em>of the stone above the ground when it reaches the wall is given by,

$h_1=h-y\\ =(2.4m)-(0.784m)\\ =1.616m=1.62m$

When the stone reaches the wall, its height from the ground is <u>1.62m.</u>

The stone thus crosses over the wall, since the height of the wall is 1 m. It reaches the ground at a distance <em>R</em> from the point of projection. If the time taken by the stone to reach the ground is <em>t₁, </em>then,

$h=\frac{1}{2} gt_1^2$

Calculate the time taken by the stone to reach the ground.

$t_1=\sqrt{\frac{2h}{g} } \\=\sqrt{\frac{2(2.4m)}{9.81m/s^2} } \\ =0.699 s$

The horizontal distance traveled by the stone is given by,

$R=ut_1 \\ =(35m/s)(0.699s)\\ =24.5m$

The stone lands at point 24.5 m from the point of projection and 10.5 m from the wall.

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2 years ago

The suspension cable of a 1,000 kg elevator snaps, sending the elevator moving downward through its shaft. The emergency brakes

tester [92]

Answer:

option (E) 1,000,000 J

Explanation:

Given:

Mass of the suspension cable, m = 1,000 kg

Distance, h = 100 m

Now,

from the work energy theorem

Work done by the gravity = Work done by brake

or

mgh = Work done by brake

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

or

Work done by brake = 1000 × 10 × 100

or

Work done by brake = 1,000,000 J

this work done is the release of heat in the brakes

Hence, the correct answer is option (E) 1,000,000 J

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2 years ago

Optical tweezers use light from a laser to move single atoms and molecules around. Suppose the intensity of light from the tweez

Zanzabum

(a) $3.3\cdot 10^{-6} Pa$

The radiation pressure exerted by an electromagnetic wave on a surface that totally absorbs the radiation is given by

$p=\frac{I}{c}$

where

I is the intensity of the wave

c is the speed of light

In this problem,

$I=1000 W/m^2$

and substituting $c=3\cdot 10^8 m/s$ , we find the radiation pressure

$p=\frac{1000 W/m^2}{3\cdot 10^8 m/s}=3.3\cdot 10^{-6}Pa$

(b) $4.4\cdot 10^{-8} m/s^2$

Since we know the cross-sectional area of the laser beam:

$A=6.65\cdot 10^{-29}m^2$

starting from the radiation pressure found at point (a), we can calculate the force exerted on a tritium atom:

$F=pa=(3.3\cdot 10^{-6}Pa)(6.65\cdot 10^{-29} m^2)=2.2\cdot 10^{-34}N$

And then, since we know the mass of the atom

$m=5.01\cdot 10^{-27}kg$

we can find the acceleration, by using Newton's second law:

$a=\frac{F}{m}=\frac{2.2\cdot 10^{-34} N}{5.01\cdot 10^{-27} kg}=4.4\cdot 10^{-8} m/s^2$

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2 years ago

B. A hydraulic jack has a ram of 20 cm diameter and a plunger of 3 cm diameter. It is used for lifting a weight of 3 tons. Find

lozanna [386]

Answer:

option (b)

Explanation:

According to the Pascal's law

F / A = f / a

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Diameter of ram, D = 20 cm, R = 20 / 2 = 10 cm

A = π R^2 = π x 100 cm^2

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diameter of plunger, d = 3 cm, r = 1.5 cm

a = π x 2.25 cm^2

Use Pascal's law

3000 / π x 100 = f / π x 2.25

f = 67.5 Kgf

4 0

2 years ago