# Question #32808

Oct 25, 2015

$\text{_38^90"Sr}$

#### Explanation:

An isotope's mass number gives the total number of protons and neutrons that can be found in said isotope's nucleus.

$\textcolor{b l u e}{\text{mass no." = "no. of protons" + "no. of neutrons}}$

In your case you know that the number of protons, which we'll call $x$, and the number of neutrons, which we'll call $y$, add up to give the isotope's mass number

$x + y = 90$

Now, you know that for a neutral atom, the number of protons it has in its nucleus must be equal to the number of electrons that surround its nucleus.

This means that for neutral atoms, you can modify the above equation to get

$\textcolor{b l u e}{\text{mass no." = overbrace("no. of electrons")^(color(red)("= no. of protons")) + "no. of neutrons}}$

In this case, you can say that the number of protons, which is equal to the number of electrons, must be

$x + 14 = y$

This means that you have

$x = y - 14$

Plug this into the equation for the mss number to get

$\left(y - 14\right) + y = 90$

$2 y = 90 + 14 \implies y = \frac{104}{2} = 52$

This isotope has $52$ neutrons in its nucleus, which implies that it also has

$x = y - 14 = 38$

protons in its nucleus.

An atom's identity is given by its atomic number, which tells you the number of protons it has in its nucleus.

In this case, you are dealing with a strontium-90 isotope

$\text{_38^90"Sr } \to$ strontium-90