How can I figure out the number of neutrons without knowing the mass number?

An
atom contains protons, neutrons and electrons. Out of these particles, only protons and neutrons
add to the mass of the atom, since electrons are relatively massless (they have very little mass
as compared to protons and neutrons). We can determine the number of neutrons by knowing the
mass number and atomic number (which is equal to the number of protons) of an
element. 

Mass number = number of neutrons + number of protons 

= number of neutrons + atomic number

Thus, number of neutrons = mass
number - atomic number

The atomic number of an element is available from the
periodic table of elements. 

If the mass number is not given to us, we can
still calculate the number of neutrons by determining the atomic mass of the element. This value
is also available from the periodic table of elements. All the elements are listed in the
periodic table with two numbers. The number on the top is the atomic number, while the number
near the bottom is the atomic mass. 

The atomic mass is the weighted average
mass of all the isotopes of an element. If we round off the atomic mass to the nearest whole
number and subtract the atomic number from it, we get the number of neutrons.

That is, number of neutrons = atomic mass (rounded to nearest whole number) - atomic
number.

For example, Carbon has an atomic number of 6 and an atomic mass of
12.0107. 

Thus, the number of neutrons in a carbon atom is:

12 (rounded off to nearest whole number) - 6 =
6.

Hope this helps.