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3 years ago

12

the half life of a certain substance is 25 years. How long will it take for a sample of this substance to decay to 90% of its or

iginal amount ...?

1 answer:

Sveta_85 [38]3 years ago

3 0

10% = 1/2 ^n
*where n is number of half lives to reach 10%

n = ln10/ln2

and multiply by 25 gives 83.05 years to 2dp

Hope this helps

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3 years ago

An open container holds ice of mass 0.555 kg at a temperature of -16.6 ∘C . The mass of the container can be ignored. Heat is su

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Answer: A. 23.59 minutes.

B. 249.65 minutes

Explanation: This question involves the concept of Latent Heat and specific heat capacities of water in solid phase.

<em>Latent heat </em><em>of fusion </em>is the total amount of heat rejected from the unit mass of water at 0 degree Celsius to convert completely into ice of 0 degree Celsius (and the heat required for vice-versa process).

<em>Specific heat capacity</em> of a substance is the amount of heat required by the unit mass of a substance to raise its temperature by 1 kelvin.

Here, <u>given that</u>:

mass of ice, m= 0.555 kg

temperature of ice, T= -16.6°C

rate of heat transfer, $q=820 J.min^{-1}$

specific heat of ice, $c_{i}= 2100 J.kg^{-1}.K^{-1}$

latent heat of fusion of ice, $L_{i}=334\times10^{3}J.kg^{-1}$

<u>Asked:</u>

1. Time require for the ice to start melting.

2. Time required to raise the temperature above freezing point.

Sol.: 1.

<u>We have the formula:</u>

$Q=mc\Delta T$

Using above equation we find the total heat required to bring the ice from -16.6°C to 0°C.

$Q= 0.555\times2100\times16.6$

$Q= 19347.3 J$

Now, we require 19347.3 joules of heat to bring the ice to 0°C and then on further addition of heat it starts melting.

∴The time required before the ice starts to melt is the time required to bring the ice to 0°C.

$t=\frac{Q}{q}$

$=\frac{19347.3}{820}$

= 23.59 minutes.

Sol.: 2.

Next we need to find the time it takes before the temperature rises above freezing from the time when heating begins.

<em>Now comes the concept of Latent heat into the play, the temperature does not starts rising for the ice as soon as it reaches at 0°C it takes significant amount of time to raise the temperature because the heat energy is being used to convert the phase of the water molecules from solid to liquid.</em>

From the above solution we have concluded that 23.59 minutes is required for the given ice to come to 0°C, now we need some extra amount of energy to convert this ice to liquid water of 0°C.

<u>We have the equation:</u> latent heat, $Q_{L}= mL_{i}$

$Q_{L}= 0.555\times334\times10^{3}= 185370 J$

<u>Now the time required for supply of 185370 J:</u>

$t=\frac{Q_{L}}{q}$

$t=\frac{185370}{820}$

t= 226.06 minutes

∴ The time it takes before the temperature rises above freezing from the time when heating begins= 226.06 + 23.59

= 249.65 minutes

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2 years ago

How does the change in the temperature of the universe provide evidence for universe expansion that supports the Big Bang Theory

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Question:

1) The universe is cooling which, according to the Big Bang Theory, is expected to happen as the cosmos accumulates.

2) The universe is warming which, according to the Big Bang Theory, is expected to happen as the cosmos disperses.

3) The universe is cooling which, according to the Big Bang Theory, is expected to happen as the cosmos disperses.

4) The universe is warming which, according to the Big Bang Theory, is expected to happen as the cosmos accumulates.

Answer:

The correct option is;

3) The Universe is cooling which, according to the Big Bang Theory, is expected to happen as the cosmos disperses

Explanation:

With the temperature measurement carried out using the CSIRO radio telescope, Astronomers have been able to determine a temperature difference in the universe from 5.08 Kelvin 7.2 billion light years away to 2.73 Kelvin in the Universe today, which is in support of the Big Bang theory that as the Universe expanded from a state of extreme temperature that cools down as the Universe expands or the cosmos disperses.

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2 years ago

A racecar accelerates from rest at 6.5 m/s2 for 4.1 s. How fast will it be going at the end of that time?

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Answer:

The final velocity of the car is 26.65 m/s.

Explanation:

Given;

acceleration of the racecar, a = 6.5 m/s²

initial velocity of the car, u = 0

time of motion, t = 4.1 s

The final velocity of the car is given by;

v = u + at

where;

v is the final velocity of the car

suvstitute the givens

v = 0 + (6.5)(4.1)

v = 26.65 m/s.

Therefore, the final velocity of the car is 26.65 m/s.

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2 years ago