Answer:
N = 3982 times
Explanation:
At the hydrogen ground state, the probability density is given by
[tex]P(r) = \frac{4r^{2} }{a_{0} ^{3} } e^{\frac{-2r}{a_{0} } }[/tex]
The number of times the atomic electron is observed at a distance 2a₀ from the nucleus is given by:
[tex]N = 5000 \frac{P(2a_{0} )}{P(\frac{a_{0} }{2} )}[/tex]
By simplification,
[tex]N = 5000\frac{2(a_{0}) ^{2}e^{\frac{-4a_{0} }{a_{0} } } }{ (\frac{a_{0} }{2} )^{2} e^{\frac{-a_{0} }{a_{0} }}}[/tex]
[tex]N = 5000 * 16 * e^{-3}[/tex]
N = 3982.97
N = 3982 times
