Ql. (a) Show the square of the speed of light, c\', is equivalent to 931.46 MeV

Question

Ql. (a) Show the square of the speed of light, c', is equivalent to 931.46 MeV per amu, i.c., c93.46 MeV/amu. Show all the unit conversion steps (b) Show that 1 amu is numerically equal to the reciprocal of Avogadro's number (c) How many atoms are there in 10 grams of 'C? Q2. A nuclear power plant produces 1000 MW(e) with a thermal efficiency of 32%. The "heating value" of uranium fuel when fissioned is 8.21 X 107 MJ/kg. Here, the heating value simply means the amount of nuclear energy converted to thermal energy in the fission process. How many kilograms of uranium docs the station consume per day? Q3. In a certain accelerator, 10 GeV (10 x 109 eV) electrons are produced. To put it more carefully, sufficient energy is transferred to the electron to bring its kinetic energy to T 10 GeV. An electron volt (1.60219xI0 19 J) is the energy required to raise the potential of an electron by one volt. (a) What is the mass of the electron under this condition in comparison with the rest mass, mo-9, ux10a (b) Use the relativistic mass equation to calculate the speed of the 10 GeV electron Q4. In the nuclear reactions shown below, the rest mass of the aluminum nucleus (Al) is given as 26.99007 amu, and the Q-value of each reaction is indicated. Identify the product nucleus and calculate the mass of the product nucleus 27A1 (n,y); Q 7.722 Mev TAI (d,p): Q = 5.497 Mev 5. 9°Sr decays to yttrium-90 (0Y) which also decays to zirconium-90 (0Zr). If the half lives of 9°Sr and oy are 28.1 years and 64 hours, respectively, calculate the activity (disintegration rate) of 9Y at 24 hours ifone has 1.0 Ci ofmgr and no 90Y at t = 0 06. 238U (T1/2-4.5x109 years) decays by alpha and , decays to stable 206Pb (lead) in a series of radioactive decay a) How many decays are involved? b) What is the rate of alpha particle production in a rock containing 1.0 g of 238U with all its daughters in equilibrium? c)2"Rn (Tin- 3.8 days) is a noble gas produced by the radioactive decay of28U. The daughters of2Rn are a dominant contributor to our background radiation dose. Estimate the global inventory of 222Rn (in grams) assuming that 4x10" tons of uranium are present on our planet d) Calculate the global power in Watts produced by the radioactive decay of238U Q7. Deuterium (H) comprises 0.0148 atomic % of natural hydrogen. If all the deuterium (H) in 1000 kg of water is used in d-d fusion reaction, how much energy in Mega Joules (MJ) would be produced? The average energy released per d-d fusion reaction can be taken to be 3.64 MeV

Explanation / Answer

Ans 1

Part a

As we know that

Speed if light

c = 2.99*10^8 m/s

Square both sides

c2 = (2.99*10^8 m/s)2 = 8.986 x 10^16 m2/s2

c2 = 8.986 x 10^16 m2/s2

m2/s2 = kg-m2/kg-s2 = kg-m-m/kg-s2 = N-m/kg = J/kg

c2 = 8.986 x 10^16 J/kg

We know that

1/12th mass of an atom of Carbon-12 isotope

1 amu=1.6606×1027 kg

c2 = (8.986 x 10^16 J/kg) x (1.6606×10^27 kg/amu)

= 1.4923 x 10^10 J/amu

We also know that

1 eV=1 electronic charge in C × 1 V

1 eV =1.60218×10^19 J

c2 = ( 1.4923 x 10^10 J/amu) x (1eV/1.60218×10^19 J)

= (93146537.467 eV/amu) x (1MeV/10^6eV)

c2 = 931.46 MeV/amu

Part b

1 amu = (1/12) of mass of one carbon-12 atom

1 amu=1.6606×10^27 kg

Avogadro's number = total number of atoms in 12 g of carbon-12.

NA = 6.022×10^23

1 amu = (1/12)*(12/NA) g

1 amu = 1/NA

1 amu = 1/6.022×10^23 g

1 amu = 1.6606×10^24 g x 1kg/1000g

1 amu = 1.6606×10^27 kg

Part C

Avogadro's number = total number of atoms in 12 g of carbon-12.

1 mole of carbon-12 = 6.02 x 10^23 atoms

12 g of carbon-12 = 6.02 x 10^23 atoms

10 g of carbon-12 = (6.02 x 10^23) *(10/12) atoms

= 5.019 x 10^23 atoms

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