# Daily Archives: February 7, 2021

## Compare your answer with the 3.6×10⁶ tons of coal needed to fuel a comparable coal-burning power plant

A laser-fusion fuel pellet has mass 5.0 mg and consists of equal parts (by mass) of deuterium and tritium. (a) If half the deuterons and an equal number of tritons participate in D-T fusion, how much energy is released? (b) At what rate must pellets be fused in a power plant with 3000-MW thermal power output? (c) What mass of fuel would be needed to run the plant for 1 year? Compare your answer with the 3.6×10⁶ tons of coal needed to fuel a comparable coal-burning power plant

## What was the decrease in the percent of homeless who are veterans over the 10-year period?

Exercises 1–5. A profile of the homeless in 27 selected cities, according to data compiled by the U.S. Conference of Mayors for 2004, is given in the following table.   1. What was the decrease in the percent of homeless who are veterans over the 10-year period? 2. Which of the categories increased over the 10-year period and which decreased? 3. Explain why each column does not add up to 100%. 4. What percent of the homeless were single men or single women in 1994? Did this percent increase or decrease in 2004? 5. Did the total number of homeless increase or decrease over the 10-year period?

## explore this indirect approach to particle detection by plotting the data in the table below.

1. Your roommate is writing a science-fiction novel set very far in the future, 70 Gy after the Big Bang. One of the characters is a cosmologist, and your roommate wants to know what the cosmologist will measure for the Hubble constant. What’s your answer, assuming a steady expansion rate? 2. When physicists “discover” a new particle, it isn’t by finding the particle itself in their detectors. Rather, they look for events that might indicate the particle’s decay. For a given type of event, they plot the frequency of events (number per unit energy interval) versus energy. The particle shows up as a bump or deviation from an otherwise smooth background curve. You can explore this indirect approach to particle detection by plotting the data in the table….

## Write the word name of the per capita personal income in Maine.

Exercises 73–76. The following table gives the per capita personal income in the New England states according to the U.S. Bureau of Economic Analysis.   1. Write the word name of the per capita personal income in Maine. 2. Round the per capita personal income in Massachusetts to the nearest thousand. 3. Which state has the smallest per capita personal income? 4. Does Vermont or New Hampshire have a larger per capita personal income? 5. The distance from Earth to the sun was measured and determined to be 92,875,328 miles. To the nearest million miles, what is the distance?

## Show that the range of static magnetic field strengths 0.1 to 2.0 tesla corresponds to the resonance frequencies 4.3 to 86 MHz for hydrogen.

23-1. Show that the range of static magnetic field strengths 0.1 to 2.0 tesla corresponds to the resonance frequencies 4.3 to 86 MHz for hydrogen. By using data from Table 23-1, find the corresponding resonance frequencies for 19F and 13C. 23-2 Find the number of 13C nuclei in 1 mg of pure 13C. By using the data in Table 23-1, determine the number of milligrams of 13C needed to give the same signal as a cubic millimeter of water (see Example 23-2).

## What was the total correction factor between the count rate and the activity of the system used to count 131I mounted on Mylar?

9-6. A 131I standard solution was obtained from the National Bureau of Standards (NBS). The following information was supplied concerning the solution: assay of 131I at 8 A.M., January 1, 2.09 × 104 dps/mL } 2%. On January 15 at 8 A.M., a sample of 131I was counted. This sample had been obtained from a shipment of 131I in the following manner: 20 λ (I λ = 1μL) of the shipment was diluted in a volumetric flask to 25 mL; 100 λ of this solution was diluted to 10 mL; and 50 λ of this solution was withdrawn, mounted on Mylar, dried, and counted. The dried sample provided a count rate of 4280 cpm corrected for background. At the same time (8 A.M., January 15), a 50-λ sample of the NBS standard 131I solution was mounted, dried,….

## Explain how variations in the observed counts caused by fluctuations in the sensitivity of the counting system can be compensated.

9-7. A series of radioactive samples of short half-life will be counted one per day over several days. Explain how variations in the observed counts caused by fluctuations in the sensitivity of the counting system can be compensated. 9-8. A pulse height spectrum for 131I (γ ray of 0.393 MeV) was obtained with a single-channel pulse height analyzer calibrated from 0 to 500 keV. The window width was 2%. Describe the changes in the spectrum if a. A 5% window were used b. The amplifier gain were twice as great c. The amplifier gain were half as great d. The upper discriminator of the window were removed

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## What are the estimated standard deviation and the percent estimated standard deviation of the sample count rate corrected for background?

10-8. A 2048×2048×12-bit image is compressed at 10 to 1 compression ratio. How many bits are present in the compressed image? 11-1. Suppose 3600 counts were accumulated for a sample counted for 10 minutes. Background contributed 784 counts over a counting interval of 6 minutes. a. Find the estimated standard deviation and the percent estimated standard deviation of the sample count rate uncorrected for background. b. What are the estimated standard deviation and the percent estimated standard deviation for the background count rate? c. What are the estimated standard deviation and the percent estimated standard deviation of the sample count rate corrected for background?

## Describe the researcher’s original results in terms of bias, precision, and accuracy.

11-2. A medical researcher carefully measures the length of the fetal humerus in 50 ultrasound studies by using electronically generated distance-measuring “calipers” on the display. The researcher obtains a mean value of 5.5 cm with a standard deviation of 2 mm. After the measurements have been obtained, the researcher discovers through studies of excised bone that the electronically generated caliper measurements are consistently 2% larger than the true length. a. Describe the researcher’s original results in terms of bias, precision, and accuracy. b. How can the mean and standard deviation of the original data be corrected?