Question

PLEASE HELP MEEEEEEEEEE

Answer 1

symbol:
`^(71)\text{Ga}` or Ga-71

mass: 70.94 u

abundance: 39.53%

Step-by-step explanation:

We are given the following information:

• The atomic weight (average atomic mass) of the metal Gallium is 69.72 u (unified atomic mass units).
• Gallium has 2 naturally occurring isotopes.
• One of these is
  `^(69)\text{Ga}`, which has a mass of 68.9257 u and an abundance of 60.47%.

We are solving for the mass and abundance of the other isotope (
`^(71)\text{Ga}`).

First, we can calculate its abundance by subtracting the abundance of the other isotope (
`^(69)\text{Ga}`) from 100%:

`100\% - 60.47\% = \boxed{39.53\%}`

So, the abundance of the other isotope is 39.53%.

Next, we can model the average atomic mass calculation with the equation:

`\text{avg atomic mass} = (\text{mass of first})(\%\text{ first}) + (\text{mass of second})(\%\text{ second})`

↓ plugging in the known values

`19.72\text{ u} = (68.9256\text{ u})(60.47\%) + (m)(39.53\%)`

Now, we can solve for m (the mass of the second isotope) by isolating it on one side of the equation:

↓ subtracting
`(68.9256\text{ u})(60.47\%)` from both sides

`69.72\text{ u} - (68.9256\text{ u})(60.47\%) = (m)(39.53\%)`

↓ dividing both sides by 39.53%

`\frac{69.72\text{ u} - (68.9256\text{ u})(60.47\%)}{39.53\%} = m`

↓ evaluating using a calculator

`\boxed{m \approx 70.94\text{ u}}`

We can round this value to get the mass number (# protons + # neutrons) of the second isotope:

`m \approx 71`

Therefore, the symbol for the second isotope is:

`\boxed{^(71)\text{Ga}}`