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PLEASE HELP MEEEEEEEEEE

PLEASE HELP MEEEEEEEEEE-example-1
User Piscator
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Answer:

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}}

User Benck
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