is it true or false that the number of electrons in an orbital depends on the orbital's shape?
It is true. Four numbers, n, ℓ, m and s can be used to describe any electron in a stable atom.The second quantum number is the angular quantum number, ℓ. Each value of n has multiple values of ℓ ranging in values from 0 to (n-1).This quantum number determines the 'shape' of the electron cloud. In chemistry, there are names for each values of ℓ. The first value, ℓ = 0 called an s orbital. s orbitals are spherical, centered on the nucleus. The second, ℓ = 1 is called a p orbital. p orbitals are usually polar and form a teardrop petal shape with the point towards the nucleus. ℓ = 2 orbital is called a d orbital. These orbitals are similar to the p orbital shape, but with more 'petals' like a clover leaf. They can also have ring shapes around the base of the petals. The next orbital, ℓ=3 is called an f orbital. These orbitals tend to look similar to d orbitals, but with even more 'petals'. Higher values of ℓ have names that follow in alphabetical order.