The most abundant amounts by mass in the body of a healthy human adult are oxygen (61.4%), carbon (22.96%) hydrogen (10.0%) and nitrogen (2.6%). The weight which a 75 kg person would gain if all `""^(1)H` atoms are replaced by `""^(2)H` atoms is

Options

A. 15 kg
B. 37.5 kg
C. 7.5 kg
D. 10 kg

Answer

To solve the problem, we need to determine how much weight a 75 kg person would gain if all the hydrogen atoms in their body are replaced by deuterium (²H) atoms. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the mass of hydrogen in the body
Given that hydrogen constitutes 10% of a 75 kg person, we can calculate the mass of hydrogen as follows:

\[ \text{Mass of hydrogen} = \text{Total mass} \times \text{Percentage of hydrogen} \]

\[ \text{Mass of hydrogen} = 75 \, \text{kg} \times \frac{10}{100} = 7.5 \, \text{kg} \]

### Step 2: Understand the replacement of hydrogen with deuterium
In this scenario, each hydrogen atom (¹H) is replaced by a deuterium atom (²H). The mass of deuterium is approximately twice that of hydrogen. Therefore, when we replace all hydrogen atoms with deuterium, the mass of hydrogen will effectively double.

### Step 3: Calculate the new mass after replacement
Since the mass of hydrogen is 7.5 kg, when replaced by deuterium, the new mass will be:

\[ \text{New mass of deuterium} = 2 \times \text{Mass of hydrogen} = 2 \times 7.5 \, \text{kg} = 15 \, \text{kg} \]

### Step 4: Calculate the weight gain
To find the weight gain, we subtract the original mass of hydrogen from the new mass of deuterium:

\[ \text{Weight gain} = \text{New mass of deuterium} - \text{Mass of hydrogen} = 15 \, \text{kg} - 7.5 \, \text{kg} = 7.5 \, \text{kg} \]

### Step 5: Final answer
Thus, the weight that a 75 kg person would gain if all hydrogen atoms are replaced by deuterium atoms is:

\[ \text{Weight gain} = 7.5 \, \text{kg} \]

### Summary
The final answer is that the person would gain **7.5 kg**.

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