Radon Rn) is a gas. Its nucleus decays with the emission of an alpha particle to form an isotope of polonium Po): The masses of the particles are: The rest energy of a unified mass unit is 931.5 MeV. The kinetic energy of the ejected particles is

Question

Radon Rn) is a gas. Its nucleus decays with the emission of an alpha particle to form an isotope of polonium Po):  The masses of the particles are:    The rest energy of a unified mass unit is 931.5 MeV. The kinetic energy of the ejected particles is

Quizplus · Accepted Answer

The mass of Rn is 222.0175 u, and the mass of Po is 218.0068 u, so the mass difference is:
Δm = (222.0175 u - 218.0068 u) x 1.66054 x 10^-27 kg/u
Δm = 6.581 x 10^-27 kg

The kinetic energy of the alpha particle can be calculated using the equation:
KE = Δmc^2 - Q
where c is the speed of light, and Q is the energy released in the decay, which is the difference between the rest energies of the initial and final nuclei:
Q = (mRn - mPo)c^2
Q = (222.0175 u - 218.0068 u) x 931.5 MeV/u
Q = 3.74 MeV

Substituting values, we get:
KE = (6.581 x 10^-27 kg)(2.998 x 10^8 m/s)^2 - 3.74 MeV
KE = 5.49 MeV

However, since the question asks for the kinetic energy of both particles, we need to divide this value by 2:
KE = 5.49 MeV / 2 = 2.745 MeV per particle

The kinetic energy of the alpha particle is equal to its total energy, since it has zero rest mass:
KE(alpha) = 2.745 MeV

The kinetic energy of the polonium nucleus can be found by subtracting the mass of the alpha particle from the mass difference:
Δm' = (mRn - mPo - mα) = (222.0175 u - 218.0068 u - 4.0026 u) x 1.66054 x 10^-27 kg/u
Δm' = 2.622 x 10^-26 kg

The kinetic energy of the polonium nucleus is:
KE(Po) = Δm'c^2
KE(Po) = 6.16 MeV

Therefore, the answer is B) 6.16 MeV, which is the kinetic energy of the polonium nucleus.

Radon Rn) Is a Gas