Question 1

Two deuterium nuclei, , fuse to produce a helium nucleus, , and a neutron. A neutral deuterium atom has a mass of 2.014102 u; a neutral helium atom has a mass of 3.016030 u; a neutral hydrogen atom has a mass of 1.007825 u; a neutron has a mass of 1.008665 u; and a proton has a mass of 1.007277 u. How much energy is released in the process? 1 u = 931.494 MeV/c².

Accepted Answer

The answer of Two deuterium nuclei,  , fuse to...

Question 2

How much energy is released in the reaction ²H + ²H → ⁴He? [m(²H) = 2.012102 u, m(⁴He) = 4.002603 u]

Accepted Answer

The answer of How much energy is released in the...

Question 3

The isotope 99m Tc (half-life of 6.0 hours) is used in bone scans. How long does it take a quantity of 99m Tc to reduce to 1% of its initial activity?

Accepted Answer

The time it takes for a radioactive isotope to reduce to 1% of its initial activity can be calculated using the formula: $ t = \frac{t_{1/2}}{\ln(2)} \times \ln(\frac{1}{0.01}) $. For 99m Tc with a half-life of 6 hours, this calculation results in approximately 40 hours.

Question 4

The reaction ²H + ²H → ³H + ¹H releases 4.03 MeV of energy. If one kilogram of deuterium were made to go through this reaction, how much energy would be produced?

Accepted Answer

The reaction releases 4.03 MeV of energy per reaction. One kilogram of deuterium contains 6.022 × 10²⁶ atoms. Therefore, the total energy released would be:(4.03 MeV/reaction) × (6.022 × 10²⁶ atoms/kg) × (1.602 × 10^-13 J/MeV) = 9.7 × 10¹³ J

Question 5

When a neutron collides with a uranium-235 nucleus it can induce a variety of fission reactions. One such reaction is + $\rightarrow$ + + 2 . Given the following mass values: , 139.921620 u; , 93.915367 u; , 235.043924 u; , 1.008665 u what mass of uranium is needed to produce a 10-kiloton yield? 1 u = 1.660540 x 10^-27 kg; 1 kiloton = 5.0 x 10¹² J.

Accepted Answer

The answer of When a neutron collides with a uranium-235...

Question 6

Two deuterium nuclei, , fuse to produce a tritium nucleus, , and a hydrogen nucleus. A neutral deuterium atom has a mass of 2.014102 u; a neutral tritium atom has a mass of 3.016050 u; a neutral hydrogen atom has a mass of 1.007825 u; a neutron has a mass of 1.008665 u; and a proton has a mass of 1.007277 u. How much energy is released in the process? 1 u = 931.494 MeV/c².

Accepted Answer

The answer of Two deuterium nuclei,  , fuse to...

Question 7

An X-ray technician takes an average of ten X-rays per day and receives 2.5 mrad per X-ray. What is the total dose the technician receives in 250 working days?

Accepted Answer

The technician receives 2.5 mrad per X-ray and takes 10 X-rays per day, resulting in 25 mrad per day. Over 250 days, this totals 6250 mrad, which is equivalent to 6.25 rem (since 1 rem = 1000 mrad).

Question 8

If the internal temperature of the sun is 15 x 10⁶ K, what is the average kinetic energy of protons in this environment?

Accepted Answer

The average kinetic energy of particles in a gas is given by (3/2)kT, where k is the Boltzmann constant (8.617 x 10^-5 eV/K). For T = 15 x 10^6 K, the energy is approximately 1.9 keV.

Question 9

If a reactor produces an average power of 1000 MW for a year, how much ²³⁵U is used up assuming 200 MeV are released per fission?

Accepted Answer

First, we need to calculate the number of fissions that occur in the reactor in one year. We can use the following formula to do this:

Number of fissions = (Average power output × 1 year) ÷ (Energy released per fission)

We are given that the average power output is 1000 MW, which we can convert to joules per year by multiplying by the number of seconds in a year (31,536,000):

Average power output = 1000 MW = 1 × 10^9 W
Energy produced per year = 1 × 10^9 W × 31,536,000 s = 3.1536 × 10^16 J

We are also given that 200 MeV are released per fission, which we can convert to joules by using the conversion factor 1 MeV = 1.602 × 10^-13 J:

Energy released per fission = 200 MeV × 1.602 × 10^-13 J/MeV = 3.204 × 10^-11 J

Now we can use the formula to calculate the number of fissions:

Number of fissions = (3.1536 × 10^16 J) ÷ (3.204 × 10^-11 J/fission) = 9.845 × 10^26 fissions

Finally, to calculate the amount of uranium-235 used up, we need to use the following formula:

Amount of uranium-235 = (Number of fissions) ÷ (Number of atoms per mole) ÷ (Mass per mole)

The mass per mole of uranium-235 is 235 g/mol, and the number of atoms per mole can be calculated from Avogadro's number (6.022 × 10^23 atoms/mol):

Amount of uranium-235 = (9.845 × 10^26 fissions) ÷ (6.022 × 10^23 atoms/mol) ÷ (235 g/mol) = 384 kg

Therefore, the answer is (C) 384 kg.

Quiz 42: Nuclear Energy: Efects and Uses of Radiation

How much energy is released in the reaction 2H + 2H → 4He? [m(2H) = 2.012102 u, m(4He) = 4.002603 u]

The isotope 99m Tc (half-life of 6.0 hours) is used in bone scans. How long does it take a quantity of 99m Tc to reduce to 1% of its initial activity?

The reaction 2H + 2H → 3H + 1H releases 4.03 MeV of energy. If one kilogram of deuterium were made to go through this reaction, how much energy would be produced?

An X-ray technician takes an average of ten X-rays per day and receives 2.5 mrad per X-ray. What is the total dose the technician receives in 250 working days?

If the internal temperature of the sun is 15 x 106 K, what is the average kinetic energy of protons in this environment?

If a reactor produces an average power of 1000 MW for a year, how much 235U is used up assuming 200 MeV are released per fission?

How much energy is released in the reaction ²H + ²H → ⁴He? [m(²H) = 2.012102 u, m(⁴He) = 4.002603 u]

The reaction ²H + ²H → ³H + ¹H releases 4.03 MeV of energy. If one kilogram of deuterium were made to go through this reaction, how much energy would be produced?

If the internal temperature of the sun is 15 x 10⁶ K, what is the average kinetic energy of protons in this environment?

If a reactor produces an average power of 1000 MW for a year, how much ²³⁵U is used up assuming 200 MeV are released per fission?