Question

The most abundant elements by mass in the body of a healthy human adult are: Oxygen (61.4 %), Carbon (22.9 %), Hydrogen (10.0 %) and Nitrogen (2.6 %). The weight which a 75 kg person would gain if all $^1H$ atoms are replaced by $^2H$ atoms is:
(A) 37.5 kg
(B) 7.5 kg
(C) 10 kg
(D) 15 kg

Answer 1

The human body is made up from mainly protein, fat, and carbohydrates. These three components mainly consist of carbon, hydrogen and oxygen and except these three components the human body has approximately sixty percent water $\left( {{H_2}O} \right)$. In water $\left( {^1{H^{}}} \right)$ is mainly present and the deuterium $\left( {^2H} \right)$ as minor component present in the form of heavy water $\left( {{D_2}O} \right)$.
Formula used: To calculate mass gain following formula is used:

$\dfrac{{Weight\,\,of\,\,person \times Atomic\,\,mass \times Mass\,\,percentage\,\,of\,\,element}}{{100}}$

Complete step by step answer:
Given abundance of element by
Mass of oxygen = 61.4 %
Mass of carbon = 22.9 %
Mass of hydrogen = 10.0 %
Mass of nitrogen = 2.6 %
According to the question first we have to calculate the mass gain due to $\left( {^1{H^{}}} \right)$.
Mass of person = 75 kg

$\dfrac{{Weight{\text{ }}of{\text{ }}person \times Atomic\,\,mass \times \,\,Mass\,\,percentage{\text{ }}of\left( {^1H} \right)}}{{100}}$
Mass due to $^1H = \dfrac{{75 \times 10 \times 1}}{{100}} = 7.5\,\,kg$
Atoms are replaced by $^2H$.
Then the person gain wait$= \dfrac{{Weight\,\,of\,\,person \times Atomic\,\,mass\,\,of\,({\,^2}H) \times Mass\,\,Percentage\,\,of{\,^2}H}}{{100}}$
Atomic mass of $^2H = 2\,\,gram$
Mass percentage of $(^2H) = \,\,Mass\,\,percentage\,{\,^1}H$ because we replace the $^1H$ is replaced by $(^2H)$.
According to question,
$\dfrac{{75 \times 2 \times 10}}{{100}} = 15\,\,kilogram$
Gain of mass by a person due to all $^1H$ atoms are replaced by $^2H$ atoms is:
Mass gain by person = Mass due to $^2H$ - Mass due to $^1H$.
Mass gain due to $^2H$ = 15 kilogram
And mass gain due to $^1H$ = 7.5 kilogram
Net mass gain by person
= 15 - 7.5 = 7.5 kg

Hence the correct Option is (B).

Note: The human body naturally contains deuterium equivalent to about five grams of heavy water, which is harmless. When a large fraction of water more than fifty percent in higher organisms is replaced by heavy water, the result is cell dysfunction and death.