Q: A 1.0 gram sample of $$^{235}\mathrm{U}$$ undergoes fission according to $$^{235}\mathrm{U} $$+ ^{1}$$\mathrm{n} \$$rightarrow ^{141}$$\mathrm{Ba} $$+ ^{92}$$\mathrm{Kr} + 3$$ ^{1}$$\mathrm{n}. If $$the mass of $$^{235}\mathrm{U} is 235.044 g/$$mol, $$^{141}\mathrm{Ba} is 140.914 g/$$mol, $$^{92}\mathrm{Kr} is 91.926 g/$$mol, and a neutron is $$1.675 \times 10$$^{-24}$$ g, what is the energy released? (Hint: Calculate mass defect and use E$$ = $$mc^2)$$

Approximately $$8.2 \times 10$$^{10}$$ J

Question 1

Which force is responsible for holding nucleons together in the nucleus, overcoming the electrostatic repulsion between protons at short distances?

Accepted Answer

The strong nuclear force

Question 2

Given the element symbol $$\displaystyle \frac{56}{26}X$$, what is the identity of the element and the number of neutrons?

Accepted Answer

26 protons (Fe) and 30 neutrons

Question 3

Why do heavier elements require a higher neutron-to-proton ratio to be stable?

Accepted Answer

To offset increasing electrostatic repulsion between protons

Question 4

Which nuclear decay process converts a neutron into a proton and an electron, increasing the atomic number but leaving the mass number unchanged?

Accepted Answer

Beta decay

Question 5

What is the effect of positron emission on the atomic number and mass number of a nucleus?

Accepted Answer

Atomic number decreases, mass number unchanged

Question 6

Which decay mode is most likely to stabilize the nucleus of $$^{24}\mathrm{Ne}$$?

Accepted Answer

Beta emission

Question 7

A sample of $$^{208}\mathrm{Po}$$ initially weighing 20 grams decays for 4.50 years. If the half-life is 2.90 years, what is the mass remaining? Use the first-order decay law $$N = N_0$ e$$^{-kt}$$, where k$$ = \frac{\ln(2)}{t_{1/2}}$$.

Accepted Answer

8.2 grams

Question 8

Which unit is used to measure radioactivity, defined as one nuclear reaction per second?

Accepted Answer

Becquerel (Bq)

Question 9

A 30 gram sample of carbon from an archaeological dig has a radioactivity of $$3.9 	imes 10^5$ Bq. The initial decay rate of $$^{14}\mathrm{C}$$ is 5.5$$ 	imes $$10^4 Bq/g $$and the half-life is 5370 years. How old is the sample? Use $$t = \frac{1}{k} \ln\left(\frac{N_0$}{N}ight)$$, $$k = \frac{\ln(2)}{t_{1/2}}.$$

Accepted Answer

11180 years

Question 10

Why is the actual mass of a nucleus lower than the sum of the masses of its individual protons and neutrons?

Accepted Answer

The mass difference is converted to binding energy released during formation

Question 11

Calculate the binding energy for a nucleus if the mass defect is $$\Delta m = 3.40879 	imes 10$$^{-25}$$ g. Use E$$ = $$mc^2$$ with $$c = 3 	imes 10^8$ m/s and convert grams to kilograms.

Accepted Answer

$$3.07 	imes 10$$^{-11}$$ J

Question 12

Which element has the highest average binding energy per nucleon, making it the most stable nucleus according to the graph provided?

Accepted Answer

Iron-56 ($$^{56}\mathrm{Fe})$$

Question 13

In a nuclear power plant, what is the primary function of control rods?

Accepted Answer

To absorb excess neutrons and regulate the chain reaction

Question 14

What is the sign of $$\Delta E$$ for the fusion of hydrogen nuclei in the Sun?

Accepted Answer

$$\Delta E \u003e 0$$

Question 15

How are elements heavier than iron ($$^{56}\mathrm{Fe}) $$synthesized in the universe?

Accepted Answer

During supernova explosions

Question 16

Which device is used in laboratories to accelerate ions to high speeds and smash them together to form new elements?

Accepted Answer

Particle accelerator

Question 17

Why can both nuclear fission and fusion be exothermic?

Accepted Answer

Fission releases energy for heavy elements, fusion releases energy for light elements

Question 18

A 1.0 gram sample of $$^{235}\mathrm{U}$$ undergoes fission according to $$^{235}\mathrm{U} $$+ ^{1}$$\mathrm{n} \$$rightarrow ^{141}$$\mathrm{Ba} $$+ ^{92}$$\mathrm{Kr} + 3$$ ^{1}$$\mathrm{n}. If $$the mass of $$^{235}\mathrm{U} is 235.044 g/$$mol, $$^{141}\mathrm{Ba} is 140.914 g/$$mol, $$^{92}\mathrm{Kr} is 91.926 g/$$mol, and a neutron is $$1.675 	imes 10$$^{-24}$$ g, what is the energy released? (Hint: Calculate mass defect and use E$$ = $$mc^2)$$

Accepted Answer

Approximately $$8.2 	imes 10$$^{10}$$ J

Question 19

Which of the following statements best describes the band of stability for nuclei?

Accepted Answer

Stable nuclei have a neutron-to-proton ratio that increases with atomic number

Nuclear Chemistry: Structure, Reactions, and Applications

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