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(e) Find the standard deviation o of the distribution of the distance R, with mean 4, where the variance o² is defined by

(e) Find the standard deviation o of the distribution of the distance R, with mean 4, where the variance o² is defined by

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. iIf we think of an electron as a particle, the function C( p(t) dt = 1 – (2r2 + 2r + 1)e-2r is the cumulative distribution function of the distance, R, of the electron in a hydrogen atom from the center of the atom. The distance is measured in Bohr radii (1 Bohr radius = 5.29 x 10-"m.) For example, C(1) = 5e-2z 0.32 means that the electron is within 1 Bohr radius from the center of the atom 32% of the time. (a) Determine lim C(r) and interpret its meaning. (b) Find p(t) and sketch both p(t) and C(r). (c) Find the mean distance. (d) Near what value of r is an electron most likely to be found? 1 (e) Find the standard deviation o of the distribution of the distance R, with mean H, where the variance o? is defined by (t – µ)°p(t) dt
Transcribed Image Text:1. iIf we think of an electron as a particle, the function C( p(t) dt = 1 – (2r2 + 2r + 1)e-2r is the cumulative distribution function of the distance, R, of the electron in a hydrogen atom from the center of the atom. The distance is measured in Bohr radii (1 Bohr radius = 5.29 x 10-"m.) For example, C(1) = 5e-2z 0.32 means that the electron is within 1 Bohr radius from the center of the atom 32% of the time. (a) Determine lim C(r) and interpret its meaning. (b) Find p(t) and sketch both p(t) and C(r). (c) Find the mean distance. (d) Near what value of r is an electron most likely to be found? 1 (e) Find the standard deviation o of the distribution of the distance R, with mean H, where the variance o? is defined by (t – µ)°p(t) dt
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