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Fantom [35]
4 years ago
13

Some atomic processes can result in the emission of an electron from the atom. Electrons emitted in this way can have discrete v

alues of kinetic energy, which depend on the atomic energy levels. The probability that the electron has a particular value depends on interacions within the atom. Suppose a particular atomic process results in three values of the electron kinetic energy: Ψ1 has Ee = 10 eV, with probability 0.2. Ψ2 has Ee = 16 eV, with probability 0.3. Ψ3 has Ee = 34 eV, with probability 0.5. The electron's wave function can be written as a quantum superposition: Ψ = aΨ1 + bΨ2 + cΨ3 What are the magnitudes of a, b, and c?
Mathematics
1 answer:
KonstantinChe [14]4 years ago
4 0

Answer:

|a| = 0.447

|b| = 0.547

|c| = 0.707

Step-by-step explanation:

From available data

Ψ1 = Ee = 10eV probability = 0.2

Ψ2 = Ee = 16eV, probability = 0.3

Ψ3 = Ee = 34eV, probability = 0.5

The magnitude of a

= a² = 0.2

= a = √0.2

|a| = 0.447

The magnitude of b

b² = 0.3

b = √0.3

|b| = 0.547

The magnitude of c

c² = 0.5

c = √0.5

|c| = 0.707

So in conclusion we have magnitude of a = 0.447

b = 0.547

c = 0.707

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