Calculating Total Probability in Hydrogen Atom

In summary, the total probability of finding an electron in a specific energy level in a hydrogen atom is equal to 1. This is calculated by summing the probabilities of finding the electron in each energy level and is represented by the equation P = Σ|ψ<sub>n</sub>|<sup>2</sup>. The total probability is equal to 1 due to the normalization condition for wave functions. As the energy level increases, the total probability decreases, and it is not possible for the total probability to be greater than 1.
  • #1
NucEngMajor
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Homework Statement


In general, how would one calculate total probability/ in Hydrogen atom in two different states (n values)?

Homework Equations


P(r) = dP/dr = r^2R(r)^2?

The Attempt at a Solution


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  • #2
That question doesn't even make sense. It's like asking, "How do you calculate the total probability of a pair of dice?"

You calculate the probability of events, e.g., the probability of rolling a 7.
 

Related to Calculating Total Probability in Hydrogen Atom

Q1: What is the total probability of finding an electron in a specific energy level in a hydrogen atom?

The total probability of finding an electron in a specific energy level in a hydrogen atom is equal to 1. This means that the electron is guaranteed to be found in one of the energy levels within the atom.

Q2: How is the total probability of an electron in a hydrogen atom calculated?

The total probability of an electron in a hydrogen atom is calculated by summing the probabilities of finding the electron in each energy level. This can be represented by the equation P = Σ|ψn|2, where P is the total probability and ψn is the wave function of the electron in the nth energy level.

Q3: Why is the total probability of an electron in a hydrogen atom equal to 1?

The total probability of an electron in a hydrogen atom is equal to 1 because of the normalization condition for wave functions. This means that the sum of the probabilities of all possible outcomes must equal 1, ensuring that the electron is always present in the atom.

Q4: How does the total probability of an electron in a hydrogen atom change with increasing energy levels?

The total probability of an electron in a hydrogen atom decreases with increasing energy levels. This is because the probability of finding the electron in a higher energy level is lower than in a lower energy level, and all probabilities must sum to 1.

Q5: Can the total probability of an electron in a hydrogen atom be greater than 1?

No, the total probability of an electron in a hydrogen atom cannot be greater than 1. This would violate the normalization condition for wave functions and is not possible according to the laws of quantum mechanics.

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