Question

The average atomic mass of a sample of an element X is 10.8 u. Calculate the percentages of isotopes 10,5 X and 11,5X

Answer 1

Answer:

The percentage isotope of $_{5}^{10} X$ is $20\%$.

The percentage isotope of $_{5}^{11} X$ is $80\%$.

Explanation:

Given,

The average atomic mass of an element X of a sample = $10.8u$

The percentage isotope of $_{5}^{10} X$ and $_{5}^{11} X$ =?

Now,

• Let the percentage isotope of $_{5}^{10} X$ is A%.

Therefore,

• The percentage isotope of $_{5}^{11} X$ is ( 100 - A )%.

As we know,

• The average atomic mass = $\frac{Percentage isotope of 1 }{100}\times atomic mass of 1 + \frac{Percentage isotope of 2}{100}\times atomic mass of 2$

Therefore,

• The average atomic mass = $\frac{A}{100}\times 10 + \frac{100- A}{100}\times 11$
• $10.8 = \frac{A}{100}\times 10 + \frac{100- A}{100}\times 11$
• $10.8 = \frac{A}{10} + \frac{1100- 11A}{100}$
• $10.8 = \frac{10A + 1100 - 11A}{100}$
• $1080 = \frac{1100 - A}$
• $A = 20\%$

Hence, the percentage isotope of $_{5}^{10} X$ = $20\%$.

And the percentage isotope of $_{5}^{11} X$ is$( 100 - A )\%$ = $( 100 - 20 )\%$ = $80\%$.

Answer 2

Answer:

Answer:

The percentage isotope of _{5}^{10} X

5

10

X is 20\%20% .

The percentage isotope of _{5}^{11} X

5

11

X is 80\%80% .

Explanation:

Given,

The average atomic mass of an element X of a sample = 10.8u10.8u

The percentage isotope of _{5}^{10} X

5

10

X and _{5}^{11} X

5

11

X =?

Now,

Let the percentage isotope of _{5}^{10} X

5

10

X is A%.

Therefore,

The percentage isotope of _{5}^{11} X

5

11

X is ( 100 - A )%.

As we know,

The average atomic mass = \frac{Percentage isotope of 1 }{100}\times atomic mass of 1 + \frac{Percentage isotope of 2}{100}\times atomic mass of 2

100

Percentageisotopeof1

×atomicmassof1+

100

Percentageisotopeof2

×atomicmassof2

Therefore,

The average atomic mass = \frac{A}{100}\times 10 + \frac{100- A}{100}\times 11

100

A

×10+

100

100−A

×11

10.8 = \frac{A}{100}\times 10 + \frac{100- A}{100}\times 1110.8=

100

A

×10+

100

100−A

×11

10.8 = \frac{A}{10} + \frac{1100- 11A}{100}10.8=

10

A

+

100

1100−11A

10.8 = \frac{10A + 1100 - 11A}{100}10.8=

100

10A+1100−11A

1080 = \frac{1100 - A}

A = 20\%A=20%

Hence, the percentage isotope of _{5}^{10} X

5

10

X = 20\%20% .

And the percentage isotope of _{5}^{11} X

5

11

X is( 100 - A )\%(100−A)% = ( 100 - 20 )\%(100−20)% = 80\%80% .