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 5 000 of the observations.

a) In this set of trials, how many times is the atomic electron observed at a distance 2a0 from the nucleus?

Answer 1

N = 3982 times

Step-by-step explanation:

At the hydrogen ground state, the probability density is given by

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

The number of times the atomic electron is observed at a distance 2a₀ from the nucleus is given by:

`N = 5000 (P(2a_(0) ))/(P((a_(0) )/(2) ))`

By simplification,

`N = 5000\frac{2(a_(0)) ^(2)e^{(-4a_(0) )/(a_(0) ) } }{ ((a_(0) )/(2) )^(2) e^{(-a_(0) )/(a_(0) )}}`

`N = 5000 * 16 * e^(-3)`

N = 3982.97

N = 3982 times