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3 years ago

Radon-222 ( 222/86 Rn) is a radioactive gas with a half-life of 3.82 days. A gas sample contains 4.1 e 8 radon atoms initially.

Physics

1 answer:

kow [346]3 years ago

5 0

Answer :

(a) The number of radon atoms will remain after 12 days is, $4.67\times 10^7$

(b) The number of radon nuclei have decayed by this time will be, $3.6\times 10^8$

Explanation :

Half-life = 3.82 days

First we have to calculate the rate constant, we use the formula :

$k=\frac{0.693}{t_{1/2}}$

$k=\frac{0.693}{3.82\text{ days}}$

$k=1.81\times 10^{-1}\text{ days}^{-1}$

Now we have to calculate the number of radon atoms will remain after 12 days.

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

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant = $1.81\times 10^{-1}\text{ days}^{-1}$

t = time passed by the sample = 12 days

a = initially number of radon atoms = $4.1\times 10^8$

a - x = number of radon atoms left = ?

Now put all the given values in above equation, we get

$12=\frac{2.303}{1.81\times 10^{-1}}\log\frac{4.1\times 10^8}{a-x}$

$a-x=4.67\times 10^7$

Thus, the number of radon atoms will remain after 12 days is, $4.67\times 10^7$

Now we have to calculate the number of radon nuclei will have decayed by this time.

The number of radon nuclei have decayed = Initial number of radon atoms - Number of radon atoms left

The number of radon nuclei have decayed = $(4.1\times 10^8)-(4.67\times 10^7)$

The number of radon nuclei have decayed = $3.6\times 10^8$

Thus, the number of radon nuclei have decayed by this time will be, $3.6\times 10^8$

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3 years ago

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3 years ago

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Drag and drop each description into the appropriate category:

Anestetic [448]

Answer:

All of the following are already correctly categorized. This facts about these radioactive decays are true. Further, I have explained below in explanation portion.

Explanation:

Alpha Decay: Yes it cannot penetrate through paper & Yes it emits Alpha particle when an element undergoes the process of Alpha Decay. Here's how:

First of all, we need to understand why a particular element decays? why radioactive decay occurs?

It is because, everything in this universe tends to achieve its stable state. Everything put efforts to be in their stable state. Likewise, when radioactive elements like Uranium or Thorium become unstable they undergo the process of Alpha decay. As a result, they emit energy and alpha particle.

Furthermore, Alpha decay has low penetration power and it has higher mass than Beta Decay and Gamma Decay that's why it cannot travel in long distances. Hence, it cannot pass through a sheet of paper.

Beta Decay: Yes it emits electrons or positrons and Yes it can penetrate through paper but cannot penetrate through a foil. Here's how:

Till now, we are familiar that why the process of decay occurs right? in order to be stable. Like wise Beta Decay occurs and it emits beta particle and energy. The main difference between alpha decay and beta decay is that alpha particle's mass is much greater than beta particle's mass because beta particle is either a negatively charged electron or positron (a positively charged electron or anti-electron) and we know that mass electron is much smaller.

So, Beta Decay has moderate penetrate power and it's mass is much smaller that's why it can travel in longer distances and it can penetrate paper but cannot penetrate into foil.

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3 years ago

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The weight of an object four earth radii from the center of the earth is:

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Answer:

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As we know that the gravity due to earth at its surface is given as

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$g' = \frac{GM}{(4R)^2}$

so we can say that

$g' = \frac{g}{16}$

so here gravity becomes 1/16 times of the gravity due to earth on its surface

now we know that weight on the surface of earth is given as

$W = mg$

also the weight now at the given height is given by

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4 years ago

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m high

aleksandrvk [35]

Answer:

boat is approaching the dock at rate 1.007 m/s

Explanation:

Given data

dock that = 1 m

rate = 1 m/s

to find out

how fast is the boat approaching

solution

we apply here pythagoras theorem here

we know pulley is 1 m height

so horizontal distance is consider x and vertical is here 1 m

and hypotenuse is y

so here we can say

x² +1² = y² ..............1

if we differentiate w.r.t time

2x dx/dt = 2y dy/dy

x dx/dt = y dy/dt

we have given x = 8m and dy/dt is 1

so from equation 1

x² +1² = y²

y² = 8² +1²

y = $\sqrt{64 +1}$

so now

x dx/dt = y dy/dt

8 dx/dt = $\sqrt{64 +1}$ (1)

dx/dt = $\sqrt{64 +1}$ (1) /8

dx/dt = 1.007 m/s

therefore we say boat is approaching the dock at rate 1.007 m/s

3 0

4 years ago