In a certain $\gamma$ decay process, an excited neon atom emits a $\gamma$-ray that has an energy of 1.630 MeV. The neon atom in the ground state has a mass of 19.992 435 u. What is the mass of the excited neon atom?
A)17.498 658 u
B)18.746 422 u
C)19.994 185 u
D)19.999 685 u
E)20.003 185 u

Question

Quizplus · Accepted Answer

In this decay process, the excited neon atom emits a gamma ray, which means that there is no change in the atomic number or charge. Therefore, the ground state neon atom also has an atomic number of 10.

We can use the conservation of energy and mass to solve for the mass of the excited neon atom. The energy released by the decay, 1.630 MeV, is equal to the difference in mass between the excited and ground state neon atoms, Δm.

Δm = (1.630 MeV)/c^2     (where c is the speed of light)

We can convert this energy to units of mass using E=mc^2, where E is the energy in joules and m is the mass in kilograms.

1.630 MeV = (1.630 x 1.6 x 10^-13 J)/(3 x 10^8 m/s)^2 = 2.902 x 10^-28 kg

Therefore, the mass of the excited neon atom is:

m_excited = m_ground + Δm
m_excited = 19.992 435 u + 2.902 x 10^-28 kg/(1.66054 x 10^-27 kg/u)
m_excited = 19.994 185 u

The answer is C, 19.994 185 u.

In a Certain γ\gammaγ Decay Process, an Excited Neon Atom Emits A

In a Certain $\gamma$ Decay Process, an Excited Neon Atom Emits A