The atomic number of Uranium is 92 and its atomic mass is 238. How many neutrons does the most common isotope of Uranium have?

Interestingly enough, the atomic mass of this isotope is given to you as a whole number.

When this happens, you can say that the isotope's atomic mass is equal to its mass number.

As you know, an isotope's mass number tells you how many protons and neutrons it contains in its nucleus. If you take #Z# to be the atomic number of the isotope, i.e. the number of protons it has in its nucleus, you can say that

#color(blue)("mass number" = A = Z + "no. of neutrons")#

Well, if uranium's atomic number is equal to #92#, you can say that the most common isotope of uranium will contain

#color(blue)("no. of neutrons" = A - Z)#

#"no. of neutrons" = 238 - 146 = color(green)(146)#

The same approach can be applied when the atomic mass is not a whole number. For example, the atomic mass of uranium is actually #"238.029 u"#, not #"238 u"#.

In such cases, you need to round the atomic mass to the nearest integer value. This will give you the mass number of the element's most abundant isotope.

As you can see here, #"238.029 u"# can be rounded off to #"238 u"#, so the answer is the same

Uranium-238, which is the most common isotope of uranium, contains #146# neutrons in its nucleus