Question

10. If the average atomic mass of an element having two isotopes is 71, the ratio of the natural abundance
of the two isotopes of mass 70 and 74 will be
1) 4:1
2) 3:1
35:1
4) 6:1
​

Answer 1

2) 3 : 1

Answer:

let the availability of the two isotopes be x % and y % respectively.

Therefore,

A/Q,

$x\% \: of \: 70 + y\% \: of \: 74 = 71$

$\large{ \rightarrow \frac{70x}{100} + \frac{74y}{100} = 71}$

$\large{ \rightarrow \frac{70x + 74y}{100} = 71}$

$\large{ \rightarrow 70x + 74y = 7100}$

Also,

$x + y = 100$

On solving above two equations, we get :

• x = 75

• y = 25

Therefore,

required ratio

= x : y

= 75 : 25

= 3 : 1

Explanation:

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Answer 2

Answer:

Let, Percentage of the first isotope =x%

      Percentage of the second isotope =y%

     

Mass of the element = 71

Mass of  first isotope = 70

Mass of  second isotope  = 74

x% + y% =100%

Hence,x + y=100 (Equation 1)

We know that

The total mass of the element = (Percentage of natural abundance of first isotope x Mass of the first isotope)/100 + (Percentage of natural abundance of second isotope x Mass of the second isotope)/100

                                                  $71=(70* x)/100 + (74 *y)/100\\7100=70x + 74 y$(Equation 2)

                                                   

By putting the value of y=100-x in equation 2

we get,

7100=70x +74(100-x)

7100 = 70x +7400 -74x

4x = 300

     x=75

Hence, y=100 -x

             = 100-75

             =25

Hence x:y = 75:25

                 = 3:1