Question

The mass of a nucleus in its ground state is 9.9308. When the nucleus returns from an excited state to its ground state, a photon of 2.13 x 10^-18 is emitted. Which of the following is the mass of the nucleus in the excited state?

A) 59.928059
B) 9.929459
C) 59.92222
D) 59.933

Answer 1

To find the mass of the nucleus in the excited state, we need to use the equation ΔE = E2 - E1, where ΔE is the energy difference between the excited and ground states, E2 is the energy of the excited state, and E1 is the energy of the ground state. The energy of the emitted photon is equal to the energy difference between the two states, so we can use hf = ΔE to find the frequency of the photon. Since energy and frequency are related by the equation E = hf, we can use the equation m = hf/c^2 to find the mass of the nucleus in the excited state, where m is the mass of the nucleus, f is the frequency of the photon, and c is the speed of light.

Step-by-step explanation:

To find the mass of the nucleus in the excited state, we need to use the equation ΔE = E2 - E1, where ΔE is the energy difference between the excited and ground states, E2 is the energy of the excited state, and E1 is the energy of the ground state. The energy of the emitted photon is equal to the energy difference between the two states, so we can use hf = ΔE to find the frequency of the photon. Since energy and frequency are related by the equation E = hf, we can use the equation m = hf/c^2 to find the mass of the nucleus in the excited state, where m is the mass of the nucleus, f is the frequency of the photon, and c is the speed of light. Substituting the given values into these equations, we find that the mass of the nucleus in the excited state is 9.929459 units.