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Sagot :
Thus, the probability of the electron being in a spherical shell at distance (a) from the proton is e^(-a/a0), at distance (b) is e^(-b/a0), and at distance (c) is e^(-c/a0).
What is meant by probability?
Probability is a metric for determining the possibility or chance of an event happening. It is a mathematical concept that measures the unpredictability of an occurrence and is frequently stated as a decimal or fraction. For example, if the probability of flipping a coin and obtaining heads is 0.5, there is a 50% chance of flipping heads. The number of favorable outcomes to the total number of potential outcomes is used to compute probability. In other words, it is the number of ways an event may occur divided by the total number of conceivable outcomes. Probability is used to make predictions and take wise decisions in a variety of disciplines, including mathematics, science, finance, and engineering.
How to solve?
If we assume the electron is in a hydrogen 1s orbital, the probability density function is given by the square of the 1s wavefunction, which is:
p(r) = (1/πa0^3) e^(-r/a0)
P(r, r+δr) = ∫p(r')dV = ∫p(r')4πr'^2dr'
For the given distances (a), (b), and (c), the probabilities are:
P(a) = ∫p(r')4πr'^2dr' = (1/πa0^3) ∫e^(-r'/a0)4πr'^2dr' = (1/πa0^3) * 4π * a0^3 * e^(-a/a0) = e^(-a/a0)
P(b) = e^(-b/a0)
P(c) = e^(-c/a0)
To learn more about probability, visit:
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