No chance to run 64-bit software on a 32-bit CPU. One big difference between both architectures is their GPR (general purpose register). It holds data the CPU needs for its calculations. 64-bit software is optimized for using 64-bit datatypes. Those cannot fit into a 32-bit GPR...obviously There are other differences, but this one is very important.
It's like a drawer which is 32 inches long. You just cannot store an iron rod longer than 32 inches in it - but (and that's why 64-bit CPUs can work with 32-bit code) you can easily fit a 32 inch rod into a 64 inch drawer
So in short: 64-bit executables use different data type sizes and alignments, than 32-bit executables.