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amid [387]
2 years ago
11

A radioactive material has a count rate of 400 per minute. It has a half life of 40 years. How long will it take to decay to a r

ate of 25 counts per minute
Physics
1 answer:
cestrela7 [59]2 years ago
7 0

Answer:

160 years.

Explanation:

From the question given above, the following data were obtained:

Initial count rate (Cᵢ) = 400 count/min

Half-life (t½) = 40 years

Final count rate (Cբ) = 25 count/min

Time (t) =?

Next, we shall determine the number of half-lives that has elapse. This can be obtained as follow:

Initial count rate (Cᵢ) = 400 count/min

Final count rate (Cբ) = 25 count/min

Number of half-lives (n) =?

Cբ = 1/2ⁿ × Cᵢ

25 = 1/2ⁿ × 400

Cross multiply

25 × 2ⁿ = 400

Divide both side by 25

2ⁿ = 400/25

2ⁿ = 16

Express 16 in index form with 2 as the base

2ⁿ = 2⁴

n = 4

Thus, 4 half-lives has elapsed.

Finally, we shall determine the time taken for the radioactive material to decay to the rate of 25 counts per minute. This can be obtained as follow:

Half-life (t½) = 40 years

Number of half-lives (n) = 4

Time (t) =?

n = t / t½

4 = t / 40

Cross multiply

t = 4 × 40

t = 160 years.

Thus, it will take 160 years for the radioactive material to decay to the rate of 25 counts per minute.

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IMPORTANT 3 QUESTIONS!
Brums [2.3K]

Answer:

7. 20,000,000 mL.

8. 8,000 m.

9. 120,000 secs.

10. 4

Explanation:

7. Determination of the volume in millilitres (mL)

Volume in litre (L) = 20,000 L

Volume in millilitres (mL) =..?

The volume in mL can be obtained as follow:

1 L = 1,000 mL

Therefore,

20,000 L = 20,000 x 1,000 = 20,000,000 mL.

Therefore, 20,000 L is equivalent to 20,000,000 mL.

8. Determination of the distance in metre (m)

Distance in mile = 5 mile

Distance in metre =?

First, we shall convert from mile to kilometre.

This can be done as follow:

1 mile = 1.6 km

Therefore,

5 mile = 5 x 1.6 = 8 km

Finally, we shall convert 8 km to metre (m).

This is illustrated below:

1 km = 1,000 m

Therefore,

8 km = 8 x 1,000 = 8,000 m

Therefore, 5 miles is equivalent to 8,000 m.

9. Determination of the time in seconds.

Time = 400 minutes for 5 days.

First, we shall convert 400 mins to hour.

This is illustrated below:

60 minutes = 1 hour

Therefore,

400 mins = 400/60 = 20/3 hours

The time (hours) is 20/3 hours in 1 day.

Therefore, the time (hours) in 5 days will be = 20/3 x 5 = 100/3 hours.

Next, we shall convert 100/3 hours to minutes.

This is illustrated below:

1 hour = 60 minutes

Therefore,

100/3 hours = 100/3 x 60 = 2000 mins

Finally, we shall convert 2000 mins to seconds.

This is illustrated below:

1 mins = 60 secs

2000 mins = 2000 x 60 = 120,000 secs.

Therefore, the time is 120,000 secs.

10. Determination of the number of significant figures.

To obtain the significant figures of a number, we simply count all the numbers available.

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6 0
3 years ago
Can a physical change, change what a substance is
Elden [556K]
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7 0
2 years ago
1.imagine you were able to throw a ball in a frictionless environment such as outer space.once you let go of the ball,what will
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Imagine you were able to throw a ball in a frictionless environment
such as outer space.  Once you let go of the ball, it will travel forever
in a straight line, and at a constant speed.  (At least until it bumps into
something.)

A car accelerates down the road.  The reaction to the tires pushing
on the road is the road pushing on the tires.

5 0
3 years ago
Which would be the best metal to use for the insulated wire?
katrin2010 [14]
Copper, because it has the lowest specific electrical resistance.

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6 0
3 years ago
PLEASEEE HELP, thank you :)
telo118 [61]

Answer:

The answer is B.

Explanation:

Given that the <em>current </em>(Ampere) in a series circuit is same so we can ignore it. We can assume that the total voltage is 60V and all the 3 resistance are different, 20Ω, 40Ω and 60Ω. So first, we have to find the total resistance by adding :

Total resistance = 20Ω + 40Ω + 60Ω

= 120Ω

Next, we have to find out that 1Ω is equal to how many voltage by dividing :

120Ω = 60V

1Ω = 60V ÷ 120

1Ω = 0.5V

Lastly, we have to calculate the voltage at R1 so we have to multiply by 20 (R1) :

1Ω = 0.5V

20Ω = 0.5V × 20

20Ω = 10V

8 0
3 years ago
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