Excited vs. Ground state masses of atom

[danok]

1. 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?



2. I am pretty lost here. There must be a formula relating these energies to masses somewhere, but I do not know it.

 

[kuruman]

Try E = mc².

 

[kerimek]

I can provide an explanation for the concept of excited and ground state masses of an atom. Excited and ground state refer to the energy levels of an atom's electrons. When an atom absorbs energy, its electrons move to a higher energy level, creating an excited state. When the electrons release this absorbed energy, they return to their original energy level, known as the ground state.

In the given scenario, an excited neon atom emits a gamma-ray with an energy of 1.630 MeV. This energy corresponds to the difference in energy between the excited and ground state of the neon atom. Using the formula E=mc², we can calculate the mass of the excited neon atom. The energy (E) is given in MeV, so we need to convert it to joules (J) first. 1 MeV = 1.602 x 10⁻¹³ J, so 1.630 MeV = 2.61 x 10⁻¹³ J.

Now, we can rearrange the formula to solve for mass (m), which gives us m = E/c². The speed of light (c) is 2.998 x 10⁸ m/s, so we can substitute this value and the calculated energy value to get the mass of the excited neon atom.

m = (2.61 x 10⁻¹³ J)/(2.998 x 10⁸ m/s)² = 2.9 x 10⁻³⁰ kg

This is the mass of the excited neon atom. To find the mass of the ground state neon atom, we can subtract the mass difference between the two states from the given mass of the excited neon atom. The mass difference is equivalent to the mass of the emitted gamma-ray, which is also given in the question as 1.630 MeV. Following the same conversion and calculation steps as above, we get a mass difference of 2.9 x 10⁻³⁰ kg.

Therefore, the mass of the ground state neon atom can be calculated as:

19.992435 u - (2.9 x 10⁻³⁰ kg) = 19.992435 u - 2.6 x 10⁻³⁰ u = 19.992432 u

In conclusion, the mass of the excited neon atom is 2.9 x 10⁻