Question #b9cd5

The idea here is that you need to be familiar with how isotope notation works.

So, the problem provides you with four atoms

#""_ 4^8"Fs" " " ""_ 5^8"Fs" " " ""_ 4^9"Fs" " " ""_ (color(white)(1)6)^11"Fs"#

As you can see, the number of protons present in the nucleus of a given atom, which is, of course, equal to the atomic number of the element, is always added to the bottom-left of the chemical symbol.

This means that #""_ 4^8"Fs"# and # ""_ 4^9"Fs"# are a match for point (a) because they both have #4# protons inside the nucleus.

The mass number of the atom, which tells you how many protons and neutrons are present inside the nucleus, is added to the top-left of the chemical symbol.

This means that #""_ 4^8"Fs"# and #""_ 5^8"Fs"# are a match for point (b) because they both have a mass number equal to #8#.

Now, in order for two atoms to be isotopes, they must have the same atomic number and different mass numbers. This implies that they have the same number of protons inside the nucleus, but that the number of neutrons differs.

As you can see, the two atoms that were a match for point (a) are a match for point (c) as well because they have the same atomic number, i.e. #4#, but different mass numbers, i.e. #8# and #9#, respectively.

Finally, you know that the number of neutrons present in the nucleus is given by

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

This means that in order for two atoms to have the same number of neutrons, they must have the same value for #A - Z#. This time, #""_ 4^9"Fs"# and #""_ (color(white)(1)6)^11"Fs"# are a match for point (d) because you have

#"For """_4^9"Fs: " "no. of neutrons" = 9 - 4 = 5#

#"For """_ (color(white)(1)6)^11"Fs: " "no. of neutrons" = 11 - 6 = 5#