Chemistry Question #9113

LAIRENMAYUM GYAN PRAKASH MEITEI, a 18 year old male from IMPHAL asks on September 13, 2014,

I would like to know if the distance of maximum probability of finding electrons in an orbital is equal to Bohr's radius?

viewed 379 times

The answer

David Harrington answered on September 15, 2014

For the 1s orbital in a hydrogen atom, the maximum radial probability density is at the Bohr radius, a_0, which is the radius of the orbit for an n=1 electron in the old Bohr model. The radial probability density is the probability of finding the electron at a given distance from the nucleus (strictly of finding it in a thin spherical shell of radius between r and r+dr) regardless of direction. On the other hand, the maximum probability density is at the nucleus. The probability density is the probability of finding the electron at a particular location in a particular direction (strictly of finding it in a little box of volume dV at coordinates (x,y,z)).
 
To visualize the difference, think of the probability density like the heights of office buildings in a large city, with the highest buildings in the centre and getting less high going out. The chance of finding an office worker in a building is highest at the city centre than at any other location (probability density). The radial probability is like asking for the chance of finding an office worker in a building 10 km from the centre city in any direction. Although the buildings are less high there, there are more buildings 10 km from the centre because we look in all directions. The tradeoff leads to a maximum at a finite distance from the centre.
 
For other orbitals there is not a simple relationship between the radial probability density and the radius of the orbit in the old Bohr model.

Add to or comment on this answer using the form below.

Note: All submissions are moderated prior to posting.

If you found this answer useful, please consider making a small donation to science.ca.