356 PROBLEMS 



chamber, was 25 roentgens per minute. After the beam passed through 1, 2, and 

 3 mm of aluminum the intensities were 20, 15.8, and 10.3 roentgens per minute 

 respectively. Was the beam homogeneous? 



II— 1. A hospital buys 200 mg of radium element today; how much will remain 

 at the end of 10 years? 



II-2. You are given a sample of radioactive material and have found experi- 

 mentally that the activity has dropped to one-eighth of its initial value in 15 days. 

 What is its half-life? What element is it? 



II— 3. The rate of change of a radioactive element is represented by the relation 

 dN/dt = —aN, where N denotes the number of atoms present at the time t, and a is 

 the constant of proportionality. Show that this is a form of the compound-interest 

 law. 



II-4. What is the mass of 1 millicurie of radon? 



II-5. A radium emanation tube contains 100 millicuries; how many millicuries 

 are available after 48 hours? 



II-6. A radon tube on leaving Philadelphia has a strength of 100 millicuries. If 

 it arrives at your laboratory after 16 hours what is its strength? When is its strength 

 50 millicuries? 



II-7. A radon seed causes the leaf of an electroscope to fall at the rate of 120 

 divisions per minute. How fast will the leaf move 24 hours later? 



II-8. If all the radon is collected every second day from a radon extraction plant 

 containing 500 mg of radium element, what is the strength, in millicuries, of the 

 amount collected, if it is examined 2 hours after collection? 



■ t o 



II-9. What is the frequency of a gamma ray if its wavelength is 0.030 A? 



11-10. What thickness of copper will reduce the intensity of a source of gamma 

 rays by the same amount as 2 mm of lead? 



11—11. How many alpha particles are emitted by the time a single radium atom 

 has disintegrated into an atom of lead? How many beta particles? 



11—12. You are given 2 grams of radium element enclosed in a 0.5-mm platinum 

 cover. What is the tolerance distance with no lead filter if the following lead filters 

 are required to produce a tolerance dose rate of 10 -5 roentgen per second? Filter 

 thickness of 10.5 cm at 50-cm distance, 7.5 at 100-cm, 4.5 at 200-cm, 1.0 at 500-cm. 



II— 13. What is the radiation emitted by i 5 P 32 ? 



Ill— 1. How far from the eye of an observer must a scale be placed in order that 

 1 cm on the scale will subtend an angle of 1 minute of arc? 



Ans. 3438 cm. 



III-2. Halftone screens are classified by the number of dots per inch. On 

 coated book paper 200 dots per inch are usually used. If the dot pattern is to be 

 just indistinguishable at the distance of distinct vision, how coarse a screen can be 

 used? 



Ill— 3. A given circular sample of gray paper reflects 5 per cent of the incident 

 light. It is fastened to a large piece of white paper reflecting 85 per cent. At what 

 approximate brightness of the white paper will the gray patch be just visible? 



III^. An electric lamp whose intensity is 95.0 candles is placed 250 cm from a 

 wall having a diffusive reflecting power of 80 per cent. What is its brightness in 

 lamberts and in candles per square centimeter? 



III-5. If the focal length of a lens is 25.7 cm what is its power in diopters? 



Ans. 3.9 dptr. 



III-6. The static refraction of an eye is defined as the reciprocal of the distance 

 from the first principal point to the far point. A correcting spectacle lens is +10 



