Question

In an experiment, a large number of electrons are fired at a sample of neutral hydrogen atoms and observations are made of how the incident particles scatter. The electron in the ground state of a hydrogen atom is found to be momentarily at a distance a0/2 from the nucleus in 1 300 of the observations. In this set of trials, how many times is the atomic electron observed at a distance 2a0 from the nucleus?

Answer 1

N = 1036 times

Step-by-step explanation:

The radial probability density of the hydrogen ground state is given by:

`p(r) = (4r^(2) )/(a_(0) ^(3) ) e^{(-2r)/(a_(0) ) }`

`p((a_(0) )/(2) ) = (4((a_(0) )/(2) )^(2) )/(a_(0) ^(3) ) e^{(-2((a_(0) )/(2) ))/(a_(0) ) }`

`p(2a_(0) ) = (4(2a_(0)) ^(2) )/(a_(0) ^(3) ) e^{(-4a_(0) )/(a_(0) ) }`

`N = 1300(p(2a_(0)) )/(p((a_(0) )/(2) ))`

`N = 1300\frac{(2a_(0)) ^(2)e^{(-4a_(0) )/(a_(0) ) } }{((a_(0) )/(2) )^(2) e^{(-a_(0) )/(a_(0) ) }}`

`N = 1300(16) e^(-3)`

N = 1035.57

N = 1036 times