What is the mass number of an ion with 104 electrons, 157 neutrons, and a +1 charge?

An atom's mass number will tell you how many protons and neutrons can be found in said atom's nucleus.

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

Now, notice that the question provides the number of neutrons, but that it doesn't tell you directly how many protons the atom has in its nucleus.

Instead, it tells you that you're dealing with an ion that has a #+1# charge and a total number of #104# electrons surrounding its nucleus.

As you know, a neutral atom has equal numbers of protons, which are positively charged, and electrons, which are negatively charged.

When an imbalance in the number of protons and electrons occurs, the atom becomes an ion.

In your case, you know that this ion has a #+1# charge. This means that it must have one more proton that it does electrons.

In other words, the difference between the number of protons and the number of electrons gives you the atom's net charge

#color(blue)("net charge" = "no. of protons" - "no. of electrons")#

In this case, you have

#+1 = Z - 104 implies Z = 104 + 1 = 105#

Therefore, your atom has #105# protons and #157# neutrons in its nucleus, which means that it has a mass number equal to

#A = 105 + 157 = color(green)(262)#