A LevelPhysicsEdexcelExam Questions11. Nuclear RadiationRadioactivity Decay

Radioactivity Decay (Edexcel A Level Physics)

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Radioactivity Decay

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Radioactivity Decay

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1a
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A student used a Geiger-Müller (GM) tube to determine the activity of a radium source.
Radium emits α, β, and γ radiation.

He positioned the source 20 cm from the GM tube, as shown, and recorded the count for 1 minute. He repeated the measurement and calculated a mean count.

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The student recorded the following results.

Count 1 Count 2 Mean count
183 178 181

 

Criticise the student’s method for determining the count at this position.

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1b
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From his results the student determined that the activity of the source was 3.0 Bq.

Comment on his value for the activity of the source.

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2a
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Radioactive decay is often described in textbooks as a spontaneous, random process.

State what is meant by spontaneous decay.

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2b
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Explain why there is an exponential decrease in the rate of decay for a sample containing a large number of unstable nuclei.

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3a
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Phosphogypsum is a by-product in the manufacture of fertiliser. It is slightly radioactive because of the presence of radium-226, a radioisotope with a half-life of 1600 years.

It must be stored securely as long as the activity of the radium-226 it contains is greater than 0.4 Bq per gram of phosphogypsum.

i)
In a sample of 1.0 g of phosphogypsum, the activity of radium-226 is 1.3 Bq.

Calculate the number of nuclei of radium-226 in this sample.

(3)





Number of nuclei = ...............................

ii)
Calculate the time in years it would take before this sample reached the permitted level of decay rate.

(3)





Time = ..............................years

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3b
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Radium-226 decays to radon-222 by alpha emission.

Determine the energy released in MeV in the decay of a single nucleus of radium-226.

mass of radium-226 nucleus = 225.97713 u
mass of radon-222 nucleus = 221.97040 u
mass of α particle = 4.00151 u 


Energy released = .................................MeV

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4a
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An old type of camping lamp used a ‘gas mantle’. The gas mantle is heated by the gas flame on the lamp and emits a bright white light. Gas mantles used to contain thorium-230.

Thorium-230 decays by alpha emission to form an isotope of radium. A student keeps a radioactive gas mantle in a sealed polythene bag. The student suggests that over a period of a year a significant volume of helium gas will be collected, since an alpha particle is a helium nucleus.

Give reasons why the sealed plastic bag is suitable for collecting the gas. 

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4b
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A particular gas mantle contains 5.18 x 10-5 g of thorium-230.

i)
Show that the activity of the thorium-230 in the mantle is about 4.0 x 104 Bq.

230 g of thorium-230 contains 6.02 x 1023 atoms
half-life of thorium-230 = 75 400 years
number of seconds in 1 year = 3.15 x 107 

(4)

ii)
Determine the volume of helium gas that could be collected in a year as a result of alpha emission.

Assume that the temperature is 22.0°C and the pressure is 1.00 x 105 Pa.

(4)

Volume = ................................................

iii)
Calculate the root mean square speed of the atoms in the helium gas at a temperature of 22.0°C.  

(3)

Root mean square speed = .......................................

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5a
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The photograph shows a vase made of uranium glass. Uranium glass is radioactive.

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Uranium glass usually contains a maximum of 2% uranium. Uranium glass made in the early part of the 20th century can contain up to 25% uranium.

A student carried out an investigation to determine the percentage of uranium in the glass.

The student measured the count rate by placing a Geiger Muller (GM) tube against the vase at a single position. This value was used to calculate the decay rate for the whole vase.

i)
Show that the decay constant for uranium is about 5 × 10−18 s−1
half-life of uranium = 1.41 × 1017 s

(2)

ii)
Calculate the percentage of uranium, by mass, in the glass.

area of GM tube window = 6.36 × 10−5 m2
surface area of vase = 0.0177 m2
background count rate = 525 counts in 10 minutes
count rate when GM tube next to vase = 3623 counts in 5 minutes
mass of vase = 149 g
mass of uranium atom = 238 u

(6)

Percentage of uranium = ....................................................................

iii)
The uranium decays by emitting alpha particles.

Criticise the method used to determine the percentage of uranium in the vase.

(2)

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5b
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A uranium nucleus decays to thorium by emission of an alpha particle.

It can be assumed that all the energy of the decay is transferred to kinetic energy of the alpha particle.

Calculate the speed of the emitted alpha particle.

mass of uranium nucleus = 238.0003 u
mass of thorium nucleus = 233.9942 u
mass of alpha particle = 4.0015 u



Speed of alpha particle = ....................................................................

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1
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Radium is a radioactive element. The most common isotope of radium has a half-life of almost two thousand years. A sample of radium can remain at a higher temperature than its surroundings for a long period of time.

Explain how a sample of radium is able to release significant amounts of energy over a long period of time.

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