Francium is an extremely rare alkali metal, many of whose physical properties
currently remain widely unknown. however, it's atomic mass is known to be --223
grams per mole. based on this information, how many protons and neutrons can be
found in a typical francium atom?

136 neutrons

87 protons

Explanation:

A neutral atom have equal number of protons and neutrons. In other words we can say that negative and positive charges are equal in magnitude and cancel the each other. For example if neutral atom has 6 protons than it must have 6 electrons.  The number of protons or number of electrons are the atomic number of an atom while the number of protons and number of neutrons are the mass number of an atom. Every atom consist of nucleus or a positive center. The protons and neutrons are present with in the nucleus while electrons are present out side the nucleus. All these three subatomic particles construct an atom.

Example:

In Francium the number of proton and neutron can be found by subtracting the atomic number of francium from its atomic mass. The atomic number will be the number of protons and remaining will show the total number of neutrons present in  nucleus.

Atomic number is 87

Atomic mass 223

223- 87 = 136

So number of neutrons are 136 and number of protons are 87.