If we have 2 energy states, S1 and S2, each with their own number of atoms...

If we have 2 energy states, S1 and S2, each with their own number of atoms in them, N1 and N2, then the following statement is true: "The rate at which atoms spontaneously decay from S2 to S1 is equal to the product of the probability for spontaneous decay per unit time and the number of atoms in S2, N2."

Explain the relationship between rate of occurrence and probability to occur, and justify the statement.

Solutions

Expert Solution

Probability is the ratio of number of favourable outcomes and total number of outcomes.

In this case, probability that a spontaneous transition will occur from N2 to N1 per second will then be the ratio of the number of spontaneous decays happening in a second and total number of transitions that can happen from S2 in a second.

Total number of transitions that can happen for a two energy system from S2 = number of atoms in that energy state = N2

this directly implies that the rate at which atoms spontaneously decay from S2 is the product of the probability that the spontaneous emission will occur per unit time and the number of atoms in S2.

genius_generous answered 1 year ago

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