Question

Определить количество энергии при распаде 6 кг урана-235, который при бомбардировке нейтронами распадается на ядра, летящие с большими скоростями, если атом при делении дает 200 МэВ. Сколько угля потребуется для получения той же энергии, что дает распад 6 кг урана, если уголь при сгорании дает 7000 ккал/кг?

Answer 1

Количество энергии при распаде 6 кг урана-235, который при бомбардировке
нейтронами распадается на ядра, летящие с большими скоростями, если атом при
делении дает 200 МэВ. Сколько угля потребуется для получения той же энергии,
что дает распад 6 кг урана, если уголь при сгорании дает 7000 ккал/кг?

Дано m=6 кг   E1=200 МэВ    m(угля) - ?

1) найдем число атомов ( число распадов)
N= m/mo=m/M*1аем=6/235*1,67*10^-27=1,52886*10^25

2) вся энергия  Е=E1*N=200*10^6*1,53*10^25=3,06*10^33 эВ=3.06*10^33*1,6*10^-19=
=4,896*10^14 Дж
1кал=4.2 Дж
1ккал=4200 Дж

Q= 4,896*10^14/4,2*10^3=1,1657*10^11 ккал

3) найдем массу угля   m= Q/q=1,1657*10^11/7*10^3=0,1665*10^8 кг=1,665*10^4 т

Answer 2

Calculation of Energy Released in the Decay of 6 kg of Uranium-235

To determine the amount of energy released in the decay of 6 kg of uranium-235, we need to know the energy released per atom during the fission process. According to the information provided, each atom of uranium-235 releases 200 MeV (million electron volts) of energy during fission.

To calculate the total energy released, we need to convert the mass of uranium-235 into the number of atoms. The molar mass of uranium-235 is approximately 235 g/mol. Therefore, the number of moles of uranium-235 can be calculated as follows:

Number of moles of uranium-235 = mass of uranium-235 / molar mass of uranium-235

Given that the mass of uranium-235 is 6 kg (6000 g), we can calculate the number of moles:

Number of moles of uranium-235 = 6000 g / 235 g/mol

Now, we can calculate the total energy released:

Total energy released = Number of moles of uranium-235 * Energy released per atom

Let's perform the calculations:

Number of moles of uranium-235 = 6000 g / 235 g/mol = 25.53 mol

Total energy released = 25.53 mol * 200 MeV/mol

To convert MeV to joules, we can use the conversion factor: 1 MeV = 1.60218 x 10^-13 joules.

Total energy released = 25.53 mol * 200 MeV/mol * 1.60218 x 10^-13 joules/MeV

Now, let's calculate the total energy released:

Total energy released = 25.53 mol * 200 MeV/mol * 1.60218 x 10^-13 joules/MeV

Total energy released = 8.165 x 10^11 joules

Therefore, the total energy released in the decay of 6 kg of uranium-235 is approximately 8.165 x 10^11 joules.

Calculation of Coal Required to Generate the Same Amount of Energy

To determine the amount of coal required to generate the same amount of energy as the decay of 6 kg of uranium-235, we need to know the energy content of coal.

According to the information provided, coal has an energy content of 7000 kcal/kg (kilocalories per kilogram).

To calculate the mass of coal required, we can use the following formula:

Mass of coal required = Total energy required / Energy content of coal

Given that the total energy required is 8.165 x 10^11 joules and the energy content of coal is 7000 kcal/kg, we need to convert the energy content of coal from kcal to joules.

1 kcal = 4184 joules.

Energy content of coal = 7000 kcal/kg * 4184 joules/kcal

Now, let's calculate the mass of coal required:

Mass of coal required = 8.165 x 10^11 joules / (7000 kcal/kg * 4184 joules/kcal)

Mass of coal required = 2.34 x 10^7 kg

Therefore, approximately 23.4 million kilograms (or 23,400 metric tons) of coal would be required to generate the same amount of energy as the decay of 6 kg of uranium-235.

Please note that these calculations are based on the information provided and may vary depending on the specific properties of the uranium-235 and coal used.