Concept explainers
(a)
An expression for the probability that an electron in ground state will be found outside a sphere of radius
(a)
Answer to Problem 78AP
The expression for the probability that an electron in ground state will be found outside a sphere of radius
Explanation of Solution
Write the expression for the radial probability density function for the Hydrogen atom in ground state.
Here,
Write the expression to find the probability to for an electron in grounds state to be found outside a sphere of radius
The probability outside a sphere is to be found. So integration must be done from radius of sphere to infinity.
Use expression (I) in (III) to find
Integrate expression (IV) by integration by parts.
Simplify expression (V) to find
Conclusion:
Apply limits from
Therefore, the expression for the probability that an electron in ground state will be found outside a sphere of radius
(b)
Graph the relation between probability and
(b)
Answer to Problem 78AP
The graph between probability and
Explanation of Solution
The expression for probability as a function of
The expression is exponential in nature. The graph will be exponentially decreasing as the value of
Assume values between
Figure 1 below shows the plot between probability and
Conclusion:
Therefore, The graph between probability and
(c)
The value of
(c)
Answer to Problem 78AP
The value of
Explanation of Solution
The probability to detect an electron inside or outside a sphere of radius
Use expression for probability derived in part (a).
Substitute
Put
Conclusion:
Equation (VIII) is a transcendental equation. Solving it the value of
Therefore, the value of
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Chapter 42 Solutions
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