Question

The atomic weight of an unknown element, in atomic units (amu), is approximately 20% less than that of calcium, the atomic weight of calcium is 40 amu. Which of the following best approximates the atomic weight, in amu, of the unknown element?
(a) 8
(b) 20
(c) 32
(d) 48

Answer 1

Hint: Let the mass of the unknown element be x amu. It is given in the question that the mass of the unknown element is 20% less than the mass of the calcium and mass of the calcium atom is 40 amu, so we can say that 80% of the mass of the calcium is equal to x amu. So, form the equation accordingly and solve to get the value of x.

Complete step-by-step answer:
Let us start by letting the mass of the unknown element to be x amu.
Now it is given that the mass of the unknown element, i.e., x is 20% less than the mass of calcium. It is also given that the mass of calcium is 40 amu. So, if we form an equation using this data in terms of x, we get
mass of unknown element = mass of calcium – 20% of mass of calcium.
$x=40-\dfrac{20}{100}\times 40$
$\Rightarrow x=40-\dfrac{1}{5}\times 40$
$\Rightarrow x=40-8$
$\Rightarrow x=32\text{ amu}$
Therefore, we can conclude that the mass of the unknown element is equal to 32 atomic mass units. Hence, the answer to the above question is option (c).

Note: Until and unless the mass of the elements required are mentioned, don’t use it. As different isotopes of the same element show different mass. Also, if you need to use the mass of any element, use the mass of the most abandoned isotope, if not mentioned. Be careful about the calculation part and the percentage you take.