Chapter 21, Problem 1DE

(a)

Interpretation Introduction

To determine: An experimental procedure to obtain the reproducible ratio of the activity of pitchblende relative to that of pure uranium.

Answer to Problem 1DE

Solution: The radioactivity is measured by using Geiger counter.

Explanation of Solution

Pitchblende is a uranium ore with excess amount of ${\text{UO}}_{\text{2}}$ , on oxidation ${\text{UO}}_{\text{2}}$ leads to the formation of ${\text{U}}_{\text{3}}{\text{O}}_{\text{8}}$ . As uranium are a radioactive element it contains Lead, Helium and other elements in the ore. Due to the presence of one or more element pitchblende is more radioactive than uranium.

Using ion exchange chromatography, the elements present in the ore is separated out from the ore. The percentage composition and the experimental conditions such as solvent, retention factor of the ore can be determined using high performance liquid chromatography (HPLC). The observed data is used for the separation of components from the mixture. Once the components of the mixture are separated out the radioactivity is measured by using Geiger counter. The data obtained by Geiger counter is than used to calculate the ratio of the activity of pitchblende relative to pure uranium.

Conclusion

The radioactivity is measured by using Geiger counter.

(b)

Interpretation Introduction

To determine: The possibility of using a device to measure the radioactivity quantitatively and the information to be used to identify the empirical formula of the given element.

Answer to Problem 1DE

Solution: Gamma and X-ray spectroscopy, scintillation and alpha/ beta counting are used to measure the radioactivity of the sample.

Explanation of Solution

Using gamma and X-ray spectroscopy, scintillation and alpha/ beta counting the quantitative measurement of radioactivity can be calculated.

High resolution gamma/X-ray spectroscopy is used to detect the amount of element present in ore with high accuracy. By using spectral unfolding techniques the amount of isotopes present in an ore can be calculated. The emitted X-rays from radioactive nuclides is used to determine the amount of radioactivity. Sometimes, the detection of nuclide using its X-rays is not impossible as the intensity of the rays is not known. In such cases, the intensity of X-ray is estimated by using the relative intensity of the ray related with X-ray. From these values the actual X-ray intensity can be calculated.

By using alpha/beta detector the alpha/beta counting can be calculated determine. In alpha/beta detector the count rate of the sample is measured by placing the sample on an evacuated chamber. Using these equipments the activity of the sample is calculated and from the value of activity the amount of the element and the empirical formula can be calculated.

Conclusion

Gamma and X-ray spectroscopy, scintillation and alpha/ beta counting are used to measure the radioactivity of the sample.

(c)

Interpretation Introduction

To determine: The half life of the element in the sample and the possibility of different experimental constraints depending upon the different value of half-life.

Answer to Problem 1DE

Solution:

The half life is calculated by the formula,

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

High efficiency detector is needed to identify the half-life of the elements when the half life is in the order of $10$ years and $1000$ years as the change on concentration and radioactivity is too small.

Explanation of Solution

From part (b) it is concluded that the amount of activity is used to calculate the amount of radioactive element present.

The half life of radium is $1600$ years.

It is assumed that $x$ mole of the sample is disintegrating in one year and the radioactivity obtained after one year is on terms of Curie.

Therefore, the initial number of moles and the number of moles after one year is calculated. The disintegrate amount if radioactive sample is calculated by the difference in the activity.

High efficiency detector is needed to identify the half-life of the elements when the half life is in the order of $10$ years and $1000$ years as the change on concentration and radioactivity is too small.

The half-life of nuclei is calculated by the formula,

The half life is calculated by the formula,

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

Where,

• $t_{1/2}$ is the half life of the reaction.
• $k$ is the reaction rate.

Conclusion

The half life is calculated by the formula,

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

High efficiency detector is needed to identify the half-life of the elements when the half life is in the order of $10$ years and $1000$ years as the change on concentration and radioactivity is too small.

(d)

Interpretation Introduction

To determine: The type of radiation emitted by the sample in the glow of Zinc sulphide and the device used for the quantitative measure of the amount of radioactivity in a sample.

Answer to Problem 1DE

Solution: The type of radiation emitted by the sample can be detected by the movement of the particle towards the oppositely charged plate.

Phosphorimeter is used to determine the radioactivity in a sample.

Explanation of Solution

Mixture of radium and zinc sulfide is used in glow in the dark watches. Zinc sulphides glows due to alpha rays emission from radium.

Alpha particles are positively charged species, beta particles are negatively charged species and gamma particles are neutral species. Thus, the type of radiation emitted by the sample can be detected by the movement of the particle towards the oppositely charged plate.

The phenomenon of glowing of zinc sulphide even in the absence of light is called phosphorescence and phosphorimeter is used to determine the intensity of luminescent.

Conclusion

The type of radiation emitted by the sample can be detected by the movement of the particle towards the oppositely charged plate.

Phosphorimeter is used to determine the radioactivity in a sample.