Question

The average mass of a carbon atom is 12.011. Assuming you were able to pick up only one carbon unit, the chances that you would randomly get one with a mass if 12.011 is?

The answe is in %

Answer 1

The correct answer is 0%.

This is due to the fact that none of the carbon atom actually have the mass of 12.011 u.

Carbon naturally occur as three isotopes i.e., C¹², C¹³ and C¹⁴ with relative abundance 98.9 %, 1.1 % and 1 ppt respectively.

Average mass of an element = ∑ F_iA_i = F₁A₁ + F₂A₂ +F₃A₃ ……………

Where Fi is the abundance of i^th isotope in percentage and Ai is the mass of i^th isotope.

Average mass of carbon = (12 X 0.989) + (0.011 X 13) + (0.00000000001 x 14)

Average mass of carbon = 12.011

However, it is clearly visible that none of the isotope is having a mass of 12.011,

Thus, the probability has to be zero.

Take a simple example,

You have three numbers, 1, 2 and 5

The average of these number is 2.67

So what is the probability that you will get an average number?

Answer is zero as none of the number exist as 2.67.

I hope answer is clear to you.