Answer:
Step-by-step explanation:
Solution:-
- The conclusions of Bohr's study have gave us hints regarding the probability of finding an electron ( e- ) in a 3 dimensional space of a nucleus.
- In Bohr's model the the 3-dimensional was considered as a spherical shell with thickness ( t = δr ) . Where ( r ) is the absolute radius of the density of electrons ( e - ) found in the vicinity of a nucleus.
- Bohr performed several experiments to determine what is the probability of finding of finding a single electron ( e- ) in a atom around its nucleus.
- He found that the probability P of finding an electron is a function of radial distance ( r )^2 - square of its distance from nucleus and the atom's wave-function R ( r ). The probability of the distribution is given as:
- Where R ( r ) is the wave-function specific for an atom. Here we will investigate an Hydrogen atom which has an orbital configuration = 1s orbitals.
Where, , is the Bohr's radius.
- We will determine the probability P ( r ) of finding that electron in a hydrogen atom at a radial distance r = 1.1a_o.
- Determine the P ( R ) by performing an integral from the center of spherical shell i.e nucleus r = 0 to r = 1.1a_o:
- Perform integration by parts: